A012113 Expansion of e.g.f. tan(arcsin(arcsinh(x))) (odd powers only).

1, 2, 24, 552, 28032, 1778688, 212383872, 25215328512, 5734229114880, 1029078328135680, 410202091438571520, 93624495716395745280, 65377722614151010222080, 15441784659337549573324800

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Formula

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

Example

tan(arcsin(arcsinh(x))) = x + (2/3!)*x^3 + (24/5!)*x^5 + (552/7!)*x^7 + (28032/9!)*x^9 + ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Tan[ArcSin[ArcSinh[x]]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Oct 09 2012 *)

Prog

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

Crossrefs

Sequence in context: A046744 A000186 A210905 * A156525 A170904 A090732

Adjacent sequences: A012110 A012111 A012112 * A012114 A012115 A012116

Keyword

nonn

Author

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

Status

approved