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 A009252 E.g.f. exp(x*tan(x)) (even powers only). 2
 1, 2, 20, 456, 18192, 1111840, 96035136, 11101474944, 1651123634432, 306656507699712, 69472549405824000, 18838618322988648448, 6019938761233443262464, 2237523930630521828745216 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..238 FORMULA a(n)=sum(k=1..n, (binomial(2*n,k)*sum(j=k..2*n-k, binomial(j-1,k-1)*j!*(-1)^(n+j)*2^(2*n-k-j)*stirling2(2*n-k,j)))), n>0, a(0)=1. [Vladimir Kruchinin, Jun 06 2011] a(n) ~ n^(2*n-1/4) * 2^(4*n+1/4) * 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 MATHEMATICA Exp[ Tan[ x ]*x ] (* Even Part *) With[{nn=40}, Take[CoefficientList[Series[Exp[Tan[x]*x], {x, 0, nn}], x]*Range[0, nn]!, {1, -1, 2}]] (* Vaclav Kotesovec, Jan 20 2015 *) PROG (Maxima) a(n):=sum((binomial(2*n, k)*sum(binomial(j-1, k-1)*j!*(-1)^(n+j)*2^(2*n-k-j)*stirling2(2*n-k, j), j, k, 2*n-k)), k, 1, n); [Vladimir Kruchinin, Jun 06 2011] CROSSREFS Cf. A024263. Sequence in context: A012533 A009160 A188811 * A210901 A274572 A274738 Adjacent sequences:  A009249 A009250 A009251 * A009253 A009254 A009255 KEYWORD nonn AUTHOR EXTENSIONS Extended and signs tested Mar 15 1997 by Olivier Gérard. STATUS approved

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