Sequences

392,541 sequences

Expansion of e.g.f.: exp(arcsin(arcsinh(x)))=1+x+1/2!*x^2+1/3!*x^3+1/4!*x^4+9/5!*x^5...A012111
Expansion of e.g.f.: exp(arcsin(arcsinh(x)))=1+x+1/2!*x^2+1/3!*x^3+1/4!*x^4+9/5!*x^5...
arcsin(arcsin(arcsinh(x)))=x+1/3!*x^3+17/5!*x^5+337/7!*x^7+26081/9!*x^9...A012112
arcsin(arcsin(arcsinh(x)))=x+1/3!*x^3+17/5!*x^5+337/7!*x^7+26081/9!*x^9...
Expansion of e.g.f. tan(arcsin(arcsinh(x))) (odd powers only).A012113
Expansion of e.g.f. tan(arcsin(arcsinh(x))) (odd powers only).
Expansion of e.g.f. arctan(arcsin(arcsinh(x))), odd powers only.A012114
Expansion of e.g.f. arctan(arcsin(arcsinh(x))), odd powers only.
Expansion of e.g.f. of cos(arcsin(arcsinh(x))), even powers only.A012115
Expansion of e.g.f. of cos(arcsin(arcsinh(x))), even powers only.
sinh(arcsin(arcsinh(x)))=x+1/3!*x^3+9/5!*x^5+113/7!*x^7+6993/9!*x^9...A012116
sinh(arcsin(arcsinh(x)))=x+1/3!*x^3+9/5!*x^5+113/7!*x^7+6993/9!*x^9...
arcsinh(arcsin(arcsinh(x)))=x-1/3!*x^3+17/5!*x^5-449/7!*x^7+30113/9!*x^9...A012117
arcsinh(arcsin(arcsinh(x)))=x-1/3!*x^3+17/5!*x^5-449/7!*x^7+30113/9!*x^9...
tanh(arcsin(arcsinh(x)))=x-2/3!*x^3+24/5!*x^5-664/7!*x^7+36096/9!*x^9...A012118
tanh(arcsin(arcsinh(x)))=x-2/3!*x^3+24/5!*x^5-664/7!*x^7+36096/9!*x^9...
arctanh(arcsin(arcsinh(x)))=x+2/3!*x^3+32/5!*x^5+1000/7!*x^7+68480/9!*x^9...A012119
arctanh(arcsin(arcsinh(x)))=x+2/3!*x^3+32/5!*x^5+1000/7!*x^7+68480/9!*x^9...
cosh(arcsin(arcsinh(x)))=1+1/2!*x^2+1/4!*x^4+49/6!*x^6+1/8!*x^8...A012120
cosh(arcsin(arcsinh(x)))=1+1/2!*x^2+1/4!*x^4+49/6!*x^6+1/8!*x^8...
sec(arcsin(arcsinh(x)))=1+1/2!*x^2+5/4!*x^4+109/6!*x^6+3177/8!*x^8...A012121
sec(arcsin(arcsinh(x)))=1+1/2!*x^2+5/4!*x^4+109/6!*x^6+3177/8!*x^8...
sech(arcsin(arcsinh(x)))=1-1/2!*x^2+5/4!*x^4-109/6!*x^6+4073/8!*x^8...A012122
sech(arcsin(arcsinh(x)))=1-1/2!*x^2+5/4!*x^4-109/6!*x^6+4073/8!*x^8...
Expansion of e.g.f. exp(arcsin(tanh(x))).A012123
Expansion of e.g.f. exp(arcsin(tanh(x))).
arcsin(arcsin(tanh(x)))=x+4/5!*x^5+24/7!*x^7+1744/9!*x^9+61504/11!*x^11...A012124
arcsin(arcsin(tanh(x)))=x+4/5!*x^5+24/7!*x^7+1744/9!*x^9+61504/11!*x^11...
Expansion of x/ (1-4*x+16*x^2)^(3/2).A012125
Expansion of x/ (1-4*x+16*x^2)^(3/2).
arctan(arcsin(tanh(x)))=x-3/3!*x^3+49/5!*x^5-1971/7!*x^7+147457/9!*x^9...A012126
arctan(arcsin(tanh(x)))=x-3/3!*x^3+49/5!*x^5-1971/7!*x^7+147457/9!*x^9...
sinh(arcsin(tanh(x)))=x-4/5!*x^5+80/7!*x^7-2224/9!*x^9+88960/11!*x^11...A012127
sinh(arcsin(tanh(x)))=x-4/5!*x^5+80/7!*x^7-2224/9!*x^9+88960/11!*x^11...
arcsinh(arcsin(tanh(x)))=x-2/3!*x^3+24/5!*x^5-776/7!*x^7+49536/9!*x^9...A012128
arcsinh(arcsin(tanh(x)))=x-2/3!*x^3+24/5!*x^5-776/7!*x^7+49536/9!*x^9...
tanh(arcsin(tanh(x)))=x-3/3!*x^3+41/5!*x^5-1243/7!*x^7+65681/9!*x^9...A012129
tanh(arcsin(tanh(x)))=x-3/3!*x^3+41/5!*x^5-1243/7!*x^7+65681/9!*x^9...
arctanh(arcsin(tanh(x)))=x+1/3!*x^3+9/5!*x^5+169/7!*x^7+6513/9!*x^9...A012130
arctanh(arcsin(tanh(x)))=x+1/3!*x^3+9/5!*x^5+169/7!*x^7+6513/9!*x^9...
Expansion of e.g.f. cosh(arcsin(tanh(x))) (even powers only).A012131
Expansion of e.g.f. cosh(arcsin(tanh(x))) (even powers only).
Numbers z such that x*(x+1) + y*(y+1) = z*(z+1) is solvable in positive integers x,y.A012132
Numbers z such that x*(x+1) + y*(y+1) = z*(z+1) is solvable in positive integers x,y.
sech(arcsin(tanh(x)))=1-1/2!*x^2+9/4!*x^4-201/6!*x^6+8369/8!*x^8...A012133
sech(arcsin(tanh(x)))=1-1/2!*x^2+9/4!*x^4-201/6!*x^6+8369/8!*x^8...
exp(arcsin(arctanh(x)))=1+x+1/2!*x^2+4/3!*x^3+13/4!*x^4+84/5!*x^5...A012134
exp(arcsin(arctanh(x)))=1+x+1/2!*x^2+4/3!*x^3+13/4!*x^4+84/5!*x^5...
arcsin(arcsin(arctanh(x)))=x+4/3!*x^3+92/5!*x^5+5272/7!*x^7+567440/9!*x^9...A012135
arcsin(arcsin(arctanh(x)))=x+4/3!*x^3+92/5!*x^5+5272/7!*x^7+567440/9!*x^9...
Expansion of e.g.f. tan(arcsin(arctanh(x))) (odd powers only).A012136
Expansion of e.g.f. tan(arcsin(arctanh(x))) (odd powers only).
arctan(arcsin(arctanh(x))) = x + (1/3!)*x^3 + (17/5!)*x^5 + (673/7!)*x^7 + (54305/9!)*x^9 + ...A012137
arctan(arcsin(arctanh(x))) = x + (1/3!)*x^3 + (17/5!)*x^5 + (673/7!)*x^7 + (54305/9!)*x^9 + ...
cos(arcsin(arctanh(x)))=1-1/2!*x^2-11/4!*x^4-349/6!*x^6-22455/8!*x^8...A012138
cos(arcsin(arctanh(x)))=1-1/2!*x^2-11/4!*x^4-349/6!*x^6-22455/8!*x^8...
sinh(arcsin(arctanh(x)))=x+4/3!*x^3+84/5!*x^5+4208/7!*x^7+386064/9!*x^9...A012139
sinh(arcsin(arctanh(x)))=x+4/3!*x^3+84/5!*x^5+4208/7!*x^7+386064/9!*x^9...
arcsinh(arcsin(arctanh(x)))=x+2/3!*x^3+32/5!*x^5+1336/7!*x^7...A012140
arcsinh(arcsin(arctanh(x)))=x+2/3!*x^3+32/5!*x^5+1336/7!*x^7...
tanh(arcsin(arctanh(x)))=x+1/3!*x^3+9/5!*x^5+281/7!*x^7+20913/9!*x^9...A012141
tanh(arcsin(arctanh(x)))=x+1/3!*x^3+9/5!*x^5+281/7!*x^7+20913/9!*x^9...
Expansion of e.g.f. arctanh(arcsin(arctanh(x))), odd powers only.A012142
Expansion of e.g.f. arctanh(arcsin(arctanh(x))), odd powers only.
cosh(arcsin(arctanh(x)))=1+1/2!*x^2+13/4!*x^4+469/6!*x^6+33433/8!*x^8...A012143
cosh(arcsin(arctanh(x)))=1+1/2!*x^2+13/4!*x^4+469/6!*x^6+33433/8!*x^8...
sec(arcsin(arctanh(x)))=1+1/2!*x^2+17/4!*x^4+769/6!*x^6+66849/8!*x^8...A012144
sec(arcsin(arctanh(x)))=1+1/2!*x^2+17/4!*x^4+769/6!*x^6+66849/8!*x^8...
sech(arcsin(arctanh(x)))=1-1/2!*x^2-7/4!*x^4-169/6!*x^6-9199/8!*x^8...A012145
sech(arcsin(arctanh(x)))=1-1/2!*x^2-7/4!*x^4-169/6!*x^6-9199/8!*x^8...
arcsin(tan(sin(x)))=x+2/3!*x^3+16/5!*x^5+440/7!*x^7+27904/9!*x^9...A012146
arcsin(tan(sin(x)))=x+2/3!*x^3+16/5!*x^5+440/7!*x^7+27904/9!*x^9...
arctanh(tan(sin(x)))=x+3/3!*x^3+41/5!*x^5+1467/7!*x^7+100625/9!*x^9...A012147
arctanh(tan(sin(x)))=x+3/3!*x^3+41/5!*x^5+1467/7!*x^7+100625/9!*x^9...
Expansion of e.g.f. sec(tan(sin(x))), even powers only.A012148
Expansion of e.g.f. sec(tan(sin(x))), even powers only.
sech(tan(sin(x)))=1-1/2!*x^2+1/4!*x^4+47/6!*x^6-447/8!*x^8...A012149
sech(tan(sin(x)))=1-1/2!*x^2+1/4!*x^4+47/6!*x^6-447/8!*x^8...
Expansion of e.g.f. exp(tan(arcsin(x))).A012150
Expansion of e.g.f. exp(tan(arcsin(x))).
arcsin(tan(tan(x)))=x+5/3!*x^3+121/5!*x^5+7013/7!*x^7+760465/9!*x^9...A012151
arcsin(tan(tan(x)))=x+5/3!*x^3+121/5!*x^5+7013/7!*x^7+760465/9!*x^9...
arctanh(tan(tan(x)))=x+6/3!*x^3+176/5!*x^5+12240/7!*x^7...A012152
arctanh(tan(tan(x)))=x+6/3!*x^3+176/5!*x^5+12240/7!*x^7...
sec(tan(tan(x)))=1+1/2!*x^2+21/4!*x^4+1053/6!*x^6+96905/8!*x^8...A012153
sec(tan(tan(x)))=1+1/2!*x^2+21/4!*x^4+1053/6!*x^6+96905/8!*x^8...
sech(tan(tan(x))) = 1-1/2!*x^2-11/4!*x^4-253/6!*x^6-9015/8!*x^8 ... .A012154
sech(tan(tan(x))) = 1-1/2!*x^2-11/4!*x^4-253/6!*x^6-9015/8!*x^8 ... .
E.g.f.: arcsin(tan(sinh(x))) (odd powers only).A012155
E.g.f.: arcsin(tan(sinh(x))) (odd powers only).
arctanh(tan(sinh(x)))=x+5/3!*x^3+121/5!*x^5+7069/7!*x^7+763057/9!*x^9...A012156
arctanh(tan(sinh(x)))=x+5/3!*x^3+121/5!*x^5+7069/7!*x^7+763057/9!*x^9...
sec(tan(sinh(x)))=1+1/2!*x^2+17/4!*x^4+673/6!*x^6+48929/8!*x^8...A012157
sec(tan(sinh(x)))=1+1/2!*x^2+17/4!*x^4+673/6!*x^6+48929/8!*x^8...
sech(tan(sinh(x)))=1-1/2!*x^2-7/4!*x^4-73/6!*x^6-239/8!*x^8...A012158
sech(tan(sinh(x)))=1-1/2!*x^2-7/4!*x^4-73/6!*x^6-239/8!*x^8...
E.g.f.: exp(tan(arcsinh(x))).A012159
E.g.f.: exp(tan(arcsinh(x))).
sin(tan(arcsinh(x)))=x-4/5!*x^5-136/7!*x^7+272/9!*x^9-222016/11!*x^11...A012160
sin(tan(arcsinh(x)))=x-4/5!*x^5-136/7!*x^7+272/9!*x^9-222016/11!*x^11...