A024263 - OEIS

%I #11 Jan 20 2015 12:52:32

%S 0,1,4,108,4448,276560,24034752,2782112704,413640580096,

%T 76768625740032,17380983003345920,4711153236657376256,

%U 1505098422997799215104,559357234754573189828608

%N Expansion of sinh(tan(x)*x)/2.

%C Limit n->infinity A024263(n)/A009252(n) = 1/4. - _Vaclav Kotesovec_, Jan 20 2015

%H Vaclav Kotesovec, <a href="/A024263/b024263.txt">Table of n, a(n) for n = 0..238</a>

%F 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

%t Sinh[ Tan[ x ]*x ]/2 (* Even Part *)

%t 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 *)

%Y Cf. A009252, A009611.

%K nonn

%O 0,3

%A _R. H. Hardin_

%E Extended and signs tested 03/97.