Sequences

392,541 sequences

Expansion of e.g.f. arctanh(cosh(x) * log(x+1)).A012761
Expansion of e.g.f. arctanh(cosh(x) * log(x+1)).
Expansion of e.g.f.: sec(cosh(x)*log(x+1))=1+1/2!*x^2-3/3!*x^3+28/4!*x^4-160/5!*x^5...A012762
Expansion of e.g.f.: sec(cosh(x)*log(x+1))=1+1/2!*x^2-3/3!*x^3+28/4!*x^4-160/5!*x^5...
Expansion of e.g.f.: sech(cosh(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3-18/4!*x^4+60/5!*x^5...A012763
Expansion of e.g.f.: sech(cosh(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3-18/4!*x^4+60/5!*x^5...
arcsin(cosh(x)*sin(x))=x+3/3!*x^3+25/5!*x^5+1043/7!*x^7+72465/9!*x^9...A012764
arcsin(cosh(x)*sin(x))=x+3/3!*x^3+25/5!*x^5+1043/7!*x^7+72465/9!*x^9...
exp(cosh(x)*arcsin(x))=1+x+1/2!*x^2+5/3!*x^3+17/4!*x^4+65/5!*x^5...A012765
exp(cosh(x)*arcsin(x))=1+x+1/2!*x^2+5/3!*x^3+17/4!*x^4+65/5!*x^5...
sin(cosh(x)*arcsin(x))=x+3/3!*x^3-15/5!*x^5-1029/7!*x^7-46239/9!*x^9...A012766
sin(cosh(x)*arcsin(x))=x+3/3!*x^3-15/5!*x^5-1029/7!*x^7-46239/9!*x^9...
E.g.f.: arctan(cosh(x)*tan(x))=x+3/3!*x^3-35/5!*x^5-1057/7!*x^7+59865/9!*x^9...A012767
E.g.f.: arctan(cosh(x)*tan(x))=x+3/3!*x^3-35/5!*x^5-1057/7!*x^7+59865/9!*x^9...
exp(cosh(x)*arctan(x))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+20/5!*x^5...A012768
exp(cosh(x)*arctan(x))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+20/5!*x^5...
tan(cosh(x)*arctan(x))=x+3/3!*x^3+45/5!*x^5+1071/7!*x^7+69177/9!*x^9...A012769
tan(cosh(x)*arctan(x))=x+3/3!*x^3+45/5!*x^5+1071/7!*x^7+69177/9!*x^9...
-log(cosh(x)*cos(x))=-4/4!*x^4-544/8!*x^8-707584/12!*x^12...A012770
-log(cosh(x)*cos(x))=-4/4!*x^4-544/8!*x^8-707584/12!*x^12...
exp(cosh(x)*arcsinh(x))=1+x+1/2!*x^2+3/3!*x^3+9/4!*x^4+25/5!*x^5...A012771
exp(cosh(x)*arcsinh(x))=1+x+1/2!*x^2+3/3!*x^3+9/4!*x^4+25/5!*x^5...
Take every 5th term of Padovan sequence A000931, beginning with the sixth term.A012772
Take every 5th term of Padovan sequence A000931, beginning with the sixth term.
exp(cosh(x)*arctanh(x)) = 1+x+1/2!*x^2+6/3!*x^3+21/4!*x^4+100/5!*x^5...A012773
exp(cosh(x)*arctanh(x)) = 1+x+1/2!*x^2+6/3!*x^3+21/4!*x^4+100/5!*x^5...
Expansion of e.g.f. arcsin(sec(x) * log(x+1)).A012774
Expansion of e.g.f. arcsin(sec(x) * log(x+1)).
E.g.f.: arctan(sec(x)*log(x+1)) = x - 1/2!*x^2 + 3/3!*x^3 - 37/5!*x^5 + 345/6!*x^6 - ...A012775
E.g.f.: arctan(sec(x)*log(x+1)) = x - 1/2!*x^2 + 3/3!*x^3 - 37/5!*x^5 + 345/6!*x^6 - ...
Expansion of e.g.f. arcsinh(sec(x) * log(x+1)).A012776
Expansion of e.g.f. arcsinh(sec(x) * log(x+1)).
Expansion of e.g.f. arctanh(sec(x) * log(x+1)).A012777
Expansion of e.g.f. arctanh(sec(x) * log(x+1)).
Expansion of e.g.f. sec(sec(x)*log(x+1)).A012778
Expansion of e.g.f. sec(sec(x)*log(x+1)).
Expansion of e.g.f.: sech(sec(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3-18/4!*x^4+60/5!*x^5...A012779
Expansion of e.g.f.: sech(sec(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3-18/4!*x^4+60/5!*x^5...
Expansion of e.g.f. arcsin(tan(x)) (odd powers only).A012780
Expansion of e.g.f. arcsin(tan(x)) (odd powers only).
Take every 5th term of Padovan sequence A000931, beginning with the second term.A012781
Take every 5th term of Padovan sequence A000931, beginning with the second term.
exp(sec(x)*arcsin(x))=1+x+1/2!*x^2+5/3!*x^3+17/4!*x^4+85/5!*x^5...A012782
exp(sec(x)*arcsin(x))=1+x+1/2!*x^2+5/3!*x^3+17/4!*x^4+85/5!*x^5...
sin(sec(x)*arcsin(x))=x+3/3!*x^3+5/5!*x^5-889/7!*x^7-82167/9!*x^9...A012783
sin(sec(x)*arcsin(x))=x+3/3!*x^3+5/5!*x^5-889/7!*x^7-82167/9!*x^9...
arcsin(sec(x)*arcsin(x))=x+5/3!*x^3+93/5!*x^5+4545/7!*x^7+443065/9!*x^9...A012784
arcsin(sec(x)*arcsin(x))=x+5/3!*x^3+93/5!*x^5+4545/7!*x^7+443065/9!*x^9...
tan(sec(x)*arcsin(x))=x+6/3!*x^3+140/5!*x^5+7616/7!*x^7+731856/9!*x^9...A012785
tan(sec(x)*arcsin(x))=x+6/3!*x^3+140/5!*x^5+7616/7!*x^7+731856/9!*x^9...
arctan(sec(x)*arcsin(x))=x+2/3!*x^3-12/5!*x^5-432/7!*x^7+10000/9!*x^9...A012786
arctan(sec(x)*arcsin(x))=x+2/3!*x^3-12/5!*x^5-432/7!*x^7+10000/9!*x^9...
cos(sec(x)*arcsin(x))=1-1/2!*x^2-15/4!*x^4-345/6!*x^6-11263/8!*x^8...A012787
cos(sec(x)*arcsin(x))=1-1/2!*x^2-15/4!*x^4-345/6!*x^6-11263/8!*x^8...
sinh(sec(x)*arcsin(x))=x+5/3!*x^3+85/5!*x^5+3201/7!*x^7+204905/9!*x^9...A012788
sinh(sec(x)*arcsin(x))=x+5/3!*x^3+85/5!*x^5+3201/7!*x^7+204905/9!*x^9...
arcsinh(sec(x)*arcsin(x))=x+3/3!*x^3+13/5!*x^5+7/7!*x^7+5465/9!*x^9...A012789
arcsinh(sec(x)*arcsin(x))=x+3/3!*x^3+13/5!*x^5+7/7!*x^7+5465/9!*x^9...
tanh(sec(x)*arcsin(x))=x+2/3!*x^3-20/5!*x^5-1104/7!*x^7-23728/9!*x^9...A012790
tanh(sec(x)*arcsin(x))=x+2/3!*x^3-20/5!*x^5-1104/7!*x^7-23728/9!*x^9...
arctanh(sec(x)*arcsin(x))=x+6/3!*x^3+148/5!*x^5+9184/7!*x^7...A012791
arctanh(sec(x)*arcsin(x))=x+6/3!*x^3+148/5!*x^5+9184/7!*x^7...
cosh(sec(x)*arcsin(x))=1+1/2!*x^2+17/4!*x^4+505/6!*x^6+25153/8!*x^8...A012792
cosh(sec(x)*arcsin(x))=1+1/2!*x^2+17/4!*x^4+505/6!*x^6+25153/8!*x^8...
sec(sec(x)*arcsin(x))=1+1/2!*x^2+21/4!*x^4+885/6!*x^6+67753/8!*x^8...A012793
sec(sec(x)*arcsin(x))=1+1/2!*x^2+21/4!*x^4+885/6!*x^6+67753/8!*x^8...
sech(sec(x)*arcsin(x))=1-1/2!*x^2-11/4!*x^4-85/6!*x^6+4457/8!*x^8...A012794
sech(sec(x)*arcsin(x))=1-1/2!*x^2-11/4!*x^4-85/6!*x^6+4457/8!*x^8...
arcsin(sec(x)*tan(x))=x+6/3!*x^3+120/5!*x^5+6216/7!*x^7+652800/9!*x^9...A012795
arcsin(sec(x)*tan(x))=x+6/3!*x^3+120/5!*x^5+6216/7!*x^7+652800/9!*x^9...
arctan(sec(x)*tan(x))=x+3/3!*x^3-15/5!*x^5-1197/7!*x^7-255/9!*x^9...A012796
arctan(sec(x)*tan(x))=x+3/3!*x^3-15/5!*x^5-1197/7!*x^7-255/9!*x^9...
arcsinh(sec(x)*tan(x))=x+4/3!*x^3+20/5!*x^5-296/7!*x^7-13360/9!*x^9...A012797
arcsinh(sec(x)*tan(x))=x+4/3!*x^3+20/5!*x^5-296/7!*x^7-13360/9!*x^9...
arctanh(sec(x)*tan(x))=x+7/3!*x^3+185/5!*x^5+12367/7!*x^7...A012798
arctanh(sec(x)*tan(x))=x+7/3!*x^3+185/5!*x^5+12367/7!*x^7...
sec(sec(x)*tan(x))=1+1/2!*x^2+25/4!*x^4+1177/6!*x^6+98705/8!*x^8...A012799
sec(sec(x)*tan(x))=1+1/2!*x^2+25/4!*x^4+1177/6!*x^6+98705/8!*x^8...
sech(sec(x)*tan(x))=1-1/2!*x^2-15/4!*x^4-177/6!*x^6+8225/8!*x^8...A012800
sech(sec(x)*tan(x))=1-1/2!*x^2-15/4!*x^4-177/6!*x^6+8225/8!*x^8...
exp(sec(x)*arctan(x))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+40/5!*x^5...A012801
exp(sec(x)*arctan(x))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+40/5!*x^5...
sin(sec(x)*arctan(x))=x+20/5!*x^5-784/7!*x^7+26256/9!*x^9...A012802
sin(sec(x)*arctan(x))=x+20/5!*x^5-784/7!*x^7+26256/9!*x^9...
arcsin(sec(x)*arctan(x))=x+2/3!*x^3+48/5!*x^5+1080/7!*x^7+112000/9!*x^9...A012803
arcsin(sec(x)*arctan(x))=x+2/3!*x^3+48/5!*x^5+1080/7!*x^7+112000/9!*x^9...
tan(sec(x)*arctan(x))=x+3/3!*x^3+65/5!*x^5+2051/7!*x^7+154209/9!*x^9...A012804
tan(sec(x)*arctan(x))=x+3/3!*x^3+65/5!*x^5+2051/7!*x^7+154209/9!*x^9...
arctan(sec(x)*arctan(x))=x-1/3!*x^3+33/5!*x^5-1377/7!*x^7+99649/9!*x^9...A012805
arctan(sec(x)*arctan(x))=x-1/3!*x^3+33/5!*x^5-1377/7!*x^7+99649/9!*x^9...
cos(sec(x)*arctan(x))=1-1/2!*x^2-3/4!*x^4-165/6!*x^6+1337/8!*x^8...A012806
cos(sec(x)*arctan(x))=1-1/2!*x^2-3/4!*x^4-165/6!*x^6+1337/8!*x^8...
sinh(sec(x)*arctan(x))=x+2/3!*x^3+40/5!*x^5+576/7!*x^7+46208/9!*x^9...A012807
sinh(sec(x)*arctan(x))=x+2/3!*x^3+40/5!*x^5+576/7!*x^7+46208/9!*x^9...
arcsinh(sec(x)*arctan(x))=x+28/5!*x^5-728/7!*x^7+54416/9!*x^9...A012808
arcsinh(sec(x)*arctan(x))=x+28/5!*x^5-728/7!*x^7+54416/9!*x^9...
tanh(sec(x)*arctan(x))=x-1/3!*x^3+25/5!*x^5-1209/7!*x^7+68945/9!*x^9...A012809
tanh(sec(x)*arctan(x))=x-1/3!*x^3+25/5!*x^5-1209/7!*x^7+68945/9!*x^9...
arctanh(sec(x)*arctan(x))=x+3/3!*x^3+73/5!*x^5+2779/7!*x^7...A012810
arctanh(sec(x)*arctan(x))=x+3/3!*x^3+73/5!*x^5+2779/7!*x^7...