A012136 Expansion of e.g.f. tan(arcsin(arctanh(x))) (odd powers only).

1, 5, 129, 7797, 848481, 145041093, 35799178401, 12045448529397, 5298881528389185, 2952169020073027845, 2031522244065649876545, 1692164698229362361298165, 1677876856826199251515980705

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Formula

a(n) = (2*n+1)!*sum(k=0..n, 16^(-k)*binomial(2*k,k)*(2*k+1)!*sum(i=2*k+1..2*n+1, (2^i*Stirling1(i,2*k+1)*binomial(2*n,i-1))/i!))/2. - Vladimir Kruchinin, Jun 17 2011

Example

tan(arcsin(arctanh(x))) = x + (5/3!)*x^3 + (129/5)!*x^5 + (7797/7!)*x^7 + (848481/9!)*x^9 + ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Tan[ArcSin[ArcTanh[x]]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, May 08 2024 *)

Prog

(Maxima)
a(n):=(2*n+1)!*sum(16^(-k)*binomial(2*k, k)*(2*k+1)!*sum((2^i*stirling1(i, 2*k+1)*binomial(2*n, i-1))/i!, i, 2*k+1, 2*n+1), k, 0, n)/2; /* Vladimir Kruchinin, Jun 17 2011 */

Crossrefs

Sequence in context: A230303 A094074 A012218 * A012022 A012176 A012187

Adjacent sequences: A012133 A012134 A012135 * A012137 A012138 A012139

Keyword

nonn

Author

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

Status

approved