A003716 Expansion of e.g.f. tan(sinh(x)) (odd powers only). (Formerly M3144)

1, 3, 37, 1015, 47881, 3459819, 354711853, 48961863007, 8754050024209, 1967989239505875, 543326939019354421, 180718022989699819207, 71275877445849484090393, 32890432371345908634652347, 17555593768891213894861569085

Offset

0,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..100

Formula

a(n) = Sum_{k=1..n} ((-1)^(k-1)+1)/(2^k*k!) * ( Sum_{i=0..k} (-1)^i*(k-2*i)^n *binomial(k,i) ) * ( Sum_{j=1..k} j! * 2^(k-j-1) * (-1)^((k+1)/2+j) * stirling2(k,j) ). - Vladimir Kruchinin, Apr 20 2011

a(n) ~ 4 * (2*n+1)! / (sqrt(4+Pi^2) * (log((Pi + sqrt(4+Pi^2))/2))^(2*n+2)). - Vaclav Kotesovec, Feb 16 2015

Mathematica

Tan[ Sinh[ x ] ] (* Odd Part *)
nn = 20; Table[(CoefficientList[Series[Tan[Sinh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 16 2015 *)

Prog

(Maxima)
a(n):=sum(((-1)^(k-1)+1)/(2^k*k!)*sum((-1)^i*(k-2*i)^n*binomial(k, i), i, 0, k)*(sum(j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k, j), j, 1, k)), k, 1, n); /* Vladimir Kruchinin, Apr 20 2011 */

Crossrefs

Cf. A003718, A003721.

Sequence in context: A274308 A318224 A300986 * A331345 A357398 A354334

Adjacent sequences: A003713 A003714 A003715 * A003717 A003718 A003719

Keyword

nonn

Author

R. H. Hardin

Status

approved