A024263 Expansion of sinh(tan(x)*x)/2.

0, 1, 4, 108, 4448, 276560, 24034752, 2782112704, 413640580096, 76768625740032, 17380983003345920, 4711153236657376256, 1505098422997799215104, 559357234754573189828608

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Comments

Limit n->infinity A024263(n)/A009252(n) = 1/4. - Vaclav Kotesovec, Jan 20 2015

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..238

Crossrefs

Cf. A009252, A009611.

Programs

Mathematica

Sinh[ Tan[ x ]*x ]/2 (* Even Part *)
With[{nn=40}, Take[CoefficientList[Series[Sinh[Tan[x]*x]/2, {x, 0, nn}], x] * Range[0, nn]!, {1, -1, 2}]] (* Vaclav Kotesovec, Jan 20 2015 *)

Formula

a(n) ~ n^(2*n-1/4) * 2^(4*n-7/4) * exp(2*sqrt(2*n)-2*n-1/2) / Pi^(2*n) * (1 - (Pi^2-1)/(12*sqrt(2*n))). - Vaclav Kotesovec, Jan 20 2015

Extensions

Extended and signs tested 03/97.