Sequences

392,541 sequences

Expansion of e.g.f. exp(arctan(x)-arcsinh(x)) = 1-1/3!*x^3+15/5!*x^5+10/6!*x^6-495/7!*x^7...A013461
Expansion of e.g.f. exp(arctan(x)-arcsinh(x)) = 1-1/3!*x^3+15/5!*x^5+10/6!*x^6-495/7!*x^7...
Expansion of e.g.f.: exp(arctan(x)-arctanh(x))=1-4/3!*x^3+160/6!*x^6-1440/7!*x^7...A013462
Expansion of e.g.f.: exp(arctan(x)-arctanh(x))=1-4/3!*x^3+160/6!*x^6-1440/7!*x^7...
Expansion of e.g.f. sin(arctan(x) - arctanh(x)) (odd powers only).A013463
Expansion of e.g.f. sin(arctan(x) - arctanh(x)) (odd powers only).
arctan(arctan(x)-arctanh(x))=-4/3!*x^3-1440/7!*x^7+35840/9!*x^9...A013464
arctan(arctan(x)-arctanh(x))=-4/3!*x^3-1440/7!*x^7+35840/9!*x^9...
cos(arctan(x)-arctanh(x))=1-160/6!*x^6-691200/10!*x^10+3942400/12!*x^12...A013465
cos(arctan(x)-arctanh(x))=1-160/6!*x^6-691200/10!*x^10+3942400/12!*x^12...
sec(arctan(x)-arctanh(x))=1+160/6!*x^6+691200/10!*x^10+19712000/12!*x^12...A013466
sec(arctan(x)-arctanh(x))=1+160/6!*x^6+691200/10!*x^10+19712000/12!*x^12...
Expansion of e.g.f. -log(cos(x) - log(x+1)).A013467
Expansion of e.g.f. -log(cos(x) - log(x+1)).
Expansion of e.g.f.: exp(cos(x)-exp(x))=1-x-1/2!*x^2+4/3!*x^3+5/4!*x^4-32/5!*x^5...A013468
Expansion of e.g.f.: exp(cos(x)-exp(x))=1-x-1/2!*x^2+4/3!*x^3+5/4!*x^4-32/5!*x^5...
exp(cos(x)-cosh(x))=1-2/2!*x^2+12/4!*x^4-122/6!*x^6+1792/8!*x^8...A013469
exp(cos(x)-cosh(x))=1-2/2!*x^2+12/4!*x^4-122/6!*x^6+1792/8!*x^8...
Coefficient of [x^(4*n+2)] in e.g.f. sin(cos(x) - cosh(x)).A013470
Coefficient of [x^(4*n+2)] in e.g.f. sin(cos(x) - cosh(x)).
Coefficient of [x^(4*n+2)] in e.g.f. arcsin(cosh(x) - cos(x)).A013471
Coefficient of [x^(4*n+2)] in e.g.f. arcsin(cosh(x) - cos(x)).
Coefficient of [x^(4*n+2)] in e.g.f. tan(cosh(x) - cos(x)).A013472
Coefficient of [x^(4*n+2)] in e.g.f. tan(cosh(x) - cos(x)).
arctan(cos(x)-cosh(x))=238/6!*x^6-715682/10!*x^10+12212600398/14!*x^14...A013473
arctan(cos(x)-cosh(x))=238/6!*x^6-715682/10!*x^10+12212600398/14!*x^14...
Expansion of cos(cos(x)-cosh(x)).A013474
Expansion of cos(cos(x)-cosh(x)).
Coefficient of [x^(4*n+2)] in e.g.f. sinh(cosh(x) - cos(x)).A013475
Coefficient of [x^(4*n+2)] in e.g.f. sinh(cosh(x) - cos(x)).
Coefficient of x^(4*n+2) in e.g.f. arcsinh(cos(x) - cosh(x)).A013476
Coefficient of x^(4*n+2) in e.g.f. arcsinh(cos(x) - cosh(x)).
Coefficient of [x^(4*n+2)] in expansion of e.g.f. tanh(cos(x) - cosh(x)).A013477
Coefficient of [x^(4*n+2)] in expansion of e.g.f. tanh(cos(x) - cosh(x)).
E.g.f. -arctanh(cos(x)-cosh(x)), coefficients of (4*i+2) only.A013478
E.g.f. -arctanh(cos(x)-cosh(x)), coefficients of (4*i+2) only.
cosh(cos(x)-cosh(x))=1+12/4!*x^4+1792/8!*x^8+889152/12!*x^12...A013479
cosh(cos(x)-cosh(x))=1+12/4!*x^4+1792/8!*x^8+889152/12!*x^12...
sec(cos(x)-cosh(x)) = 1+12/4!*x^4+8512/8!*x^8+41692992/12!*x^12...A013480
sec(cos(x)-cosh(x)) = 1+12/4!*x^4+8512/8!*x^8+41692992/12!*x^12...
sech(cos(x)-cosh(x)) = 1-12/4!*x^4+8288/8!*x^8-39475392/12!*x^12...A013481
sech(cos(x)-cosh(x)) = 1-12/4!*x^4+8288/8!*x^8-39475392/12!*x^12...
exp(cos(x)-sech(x))=1-4/4!*x^4+60/6!*x^6-824/8!*x^8+120/10!*x^10...A013482
exp(cos(x)-sech(x))=1-4/4!*x^4+60/6!*x^6-824/8!*x^8+120/10!*x^10...
E.g.f.: sin(cos(x)-sech(x)) (even powers only).A013483
E.g.f.: sin(cos(x)-sech(x)) (even powers only).
arcsin(cos(x)-sech(x))=-4/4!*x^4+60/6!*x^6-1384/8!*x^8+50520/10!*x^10...A013484
arcsin(cos(x)-sech(x))=-4/4!*x^4+60/6!*x^6-1384/8!*x^8+50520/10!*x^10...
tan(cos(x)-sech(x))=-4/4!*x^4+60/6!*x^6-1384/8!*x^8+50520/10!*x^10...A013485
tan(cos(x)-sech(x))=-4/4!*x^4+60/6!*x^6-1384/8!*x^8+50520/10!*x^10...
arctan(cos(x)-sech(x))=-4/4!*x^4+60/6!*x^6-1384/8!*x^8+50520/10!*x^10...A013486
arctan(cos(x)-sech(x))=-4/4!*x^4+60/6!*x^6-1384/8!*x^8+50520/10!*x^10...
cos(cos(x)-sech(x))=1-560/8!*x^8+50400/10!*x^10-4403520/12!*x^12...A013487
cos(cos(x)-sech(x))=1-560/8!*x^8+50400/10!*x^10-4403520/12!*x^12...
Expansion of e.g.f.: exp(sinh(x)-log(x+1))=1+1/2!*x^2-1/3!*x^3+9/4!*x^4-33/5!*x^5...A013488
Expansion of e.g.f.: exp(sinh(x)-log(x+1))=1+1/2!*x^2-1/3!*x^3+9/4!*x^4-33/5!*x^5...
exp(sinh(x)-arcsinh(x))=1+2/3!*x^3-8/5!*x^5+40/6!*x^6+226/7!*x^7...A013489
exp(sinh(x)-arcsinh(x))=1+2/3!*x^3-8/5!*x^5+40/6!*x^6+226/7!*x^7...
E.g.f.: exp(sinh(x)-tanh(x))=1+3/3!*x^3-15/5!*x^5+90/6!*x^6+273/7!*x^7...A013490
E.g.f.: exp(sinh(x)-tanh(x))=1+3/3!*x^3-15/5!*x^5+90/6!*x^6+273/7!*x^7...
exp(sinh(x)-arctanh(x))=1-1/3!*x^3-23/5!*x^5+10/6!*x^6-719/7!*x^7...A013491
exp(sinh(x)-arctanh(x))=1-1/3!*x^3-23/5!*x^5+10/6!*x^6-719/7!*x^7...
exp(arcsinh(x)-log(x+1)) = 1+1/2!*x^2-3/3!*x^3+9/4!*x^4-45/5!*x^5...A013492
exp(arcsinh(x)-log(x+1)) = 1+1/2!*x^2-3/3!*x^3+9/4!*x^4-45/5!*x^5...
exp(arcsinh(x)-tanh(x))=1+1/3!*x^3-7/5!*x^5+10/6!*x^6+47/7!*x^7...A013493
exp(arcsinh(x)-tanh(x))=1+1/3!*x^3-7/5!*x^5+10/6!*x^6+47/7!*x^7...
exp(arcsinh(x)-arctanh(x)) = 1-3/3!*x^3-15/5!*x^5+90/6!*x^6-945/7!*x^7...A013494
exp(arcsinh(x)-arctanh(x)) = 1-3/3!*x^3-15/5!*x^5+90/6!*x^6-945/7!*x^7...
Expansion of e.g.f.: exp(tanh(x)-log(x+1))=1+1/2!*x^2-4/3!*x^3+9/4!*x^4-48/5!*x^5...A013495
Expansion of e.g.f.: exp(tanh(x)-log(x+1))=1+1/2!*x^2-4/3!*x^3+9/4!*x^4-48/5!*x^5...
Expansion of e.g.f.: exp(tanh(x)-arctanh(x))=1-4/3!*x^3-8/5!*x^5+160/6!*x^6-992/7!*x^7...A013496
Expansion of e.g.f.: exp(tanh(x)-arctanh(x))=1-4/3!*x^3-8/5!*x^5+160/6!*x^6-992/7!*x^7...
Expansion of e.g.f. log(cosh(x)-log(x+1)).A013497
Expansion of e.g.f. log(cosh(x)-log(x+1)).
Number of permutations in S_n with a certain property.A013498
Number of permutations in S_n with a certain property.
a(n) = 2*n^n, n >= 2, otherwise a(n) = 1.A013499
a(n) = 2*n^n, n >= 2, otherwise a(n) = 1.
Expansion of e.g.f.: log(sec(x)-log(x+1))=-1*x+1/2*x^2+1/3*x^3+3/8*x^4+7/120*x^5-1/240*x^6-593/5040*x^7-37/960*x^8+...A013500
Expansion of e.g.f.: log(sec(x)-log(x+1))=-1*x+1/2*x^2+1/3*x^3+3/8*x^4+7/120*x^5-1/240*x^6-593/5040*x^7-37/960*x^8+...
Expansion of e.g.f.: exp(sec(x)-exp(x))=1-x+1/2!*x^2-2/3!*x^3+9/4!*x^4-32/5!*x^5...A013501
Expansion of e.g.f.: exp(sec(x)-exp(x))=1-x+1/2!*x^2-2/3!*x^3+9/4!*x^4-32/5!*x^5...
exp(sec(x)-cosh(x))=1+4/4!*x^4+60/6!*x^6+1944/8!*x^8+100920/10!*x^10...A013502
exp(sec(x)-cosh(x))=1+4/4!*x^4+60/6!*x^6+1944/8!*x^8+100920/10!*x^10...
E.g.f. exp(sec(x)-sech(x)) (even powers only).A013503
E.g.f. exp(sec(x)-sech(x)) (even powers only).
sin(sec(x)-sech(x))=2/2!*x^2+2/6!*x^6-176158/10!*x^10...A013504
sin(sec(x)-sech(x))=2/2!*x^2+2/6!*x^6-176158/10!*x^10...
arcsin(sec(x)-sech(x))=2/2!*x^2+242/6!*x^6+680642/10!*x^10...A013505
arcsin(sec(x)-sech(x))=2/2!*x^2+242/6!*x^6+680642/10!*x^10...
tan(sec(x) - sech(x)) = 2/2!*x^2 + 362/6!*x^6 + 1199762/10!*x^10 ...A013506
tan(sec(x) - sech(x)) = 2/2!*x^2 + 362/6!*x^6 + 1199762/10!*x^10 ...
arctan(sec(x)-sech(x))=2/2!*x^2-118/6!*x^6+211922/10!*x^10...A013507
arctan(sec(x)-sech(x))=2/2!*x^2-118/6!*x^6+211922/10!*x^10...
cos(sec(x)-sech(x))=1-12/4!*x^4-5152/8!*x^8-7351872/12!*x^12...A013508
cos(sec(x)-sech(x))=1-12/4!*x^4-5152/8!*x^8-7351872/12!*x^12...
sinh(sec(x)-sech(x))=2/2!*x^2+242/6!*x^6+438722/10!*x^10...A013509
sinh(sec(x)-sech(x))=2/2!*x^2+242/6!*x^6+438722/10!*x^10...
arcsinh(sec(x)-sech(x))=2/2!*x^2+2/6!*x^6+65762/10!*x^10...A013510
arcsinh(sec(x)-sech(x))=2/2!*x^2+2/6!*x^6+65762/10!*x^10...