A009256 - OEIS

A009256

Expansion of e.g.f. exp(tan(x)^2) (even powers only).

1, 2, 28, 872, 47248, 3907232, 454886848, 70597546112, 14042505449728, 3475021574246912, 1045247734061145088, 375054668796817221632, 158085597663328138006528, 77269840864693331267919872

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OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..235

FORMULA

a(n) = Sum_{k=1..n} (Sum_{j=2*k..2*n} binomial(j-1,2*k-1)*j!*2^(2*n-j)*(-1)^(n+k+j)*Stirling2(2*n,j)/k!). - Vladimir Kruchinin, Jun 06 2011

a(n) ~ (2*n)! * 2^(2*n+1/3) * exp(-2/3 + 4/(3*Pi^2) + (2^(4/3)*n^(1/3) + 3*n^(2/3)*(2*Pi)^(2/3))/Pi^(4/3)) / (sqrt(3) * n^(2/3) * Pi^(2*n+5/6)). - Vaclav Kotesovec, Jan 24 2015

MAPLE

S:= series(exp(tan(x)^2), x, 31):

seq(coeff(S, x, j)*j!, j=0..30, 2); # Robert Israel, Aug 07 2023

MATHEMATICA

Exp[ Tan[ x ]^2 ] (* Even Part *)

nn = 20; Table[(CoefficientList[Series[E^Tan[x]^2, {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 24 2015 *)

PROG

(Maxima)

a(n):=sum((sum(binomial(j-1, 2*k-1)*j!*2^(2*n-j)*(-1)^(n+k+j)*stirling2(2*n, j), j, 2*k, 2*n))/k!, k, 1, n); /* Vladimir Kruchinin, Jun 06 2011 */

CROSSREFS

Sequence in context: A090249 A264411 A370378 * A012725 A264637 A352251

Adjacent sequences: A009253 A009254 A009255 * A009257 A009258 A009259