A012142 Expansion of e.g.f. arctanh(arcsin(arctanh(x))), odd powers only.

1, 5, 137, 9085, 1107665, 215251189, 61040810841, 23787478734573, 12195876997744289, 7959108767371738085, 6442333032874852024617, 6333998826435424439107165, 7435387461759207059826574193, 10272314131487696006461656792277, 16499075087858185014891901869790713

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

Formula

a(n) ~ (2*n)! / (tanh(sin(1)))^(2*n+1). - Vaclav Kotesovec, Feb 05 2015

Example

x + (5/3!)*x^3 + (137/5!)*x^5 + (9085/7!)*x^7 + ...

Maple

a:= n-> (t-> t!*coeff(series(arctanh(arcsin(arctanh(x))), x, t+1), x, t))(2*n+1):
seq(a(n), n=0..15);  # Alois P. Heinz, Aug 17 2018

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[ArcTanh[x]]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 05 2015 *)

Prog

(PARI) seq(n)={my(v=Vec(serlaplace(atanh(asin(atanh(x + O(x^(2*n)))))))); vector((#v+1)\2, n, v[2*n-1])} \\ Andrew Howroyd, Aug 17 2018

Crossrefs

Sequence in context: A159546 A339566 A012215 * A012207 A192640 A192641

Adjacent sequences: A012139 A012140 A012141 * A012143 A012144 A012145

Keyword

nonn

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Status

approved