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%I #23 Jan 22 2018 03:04:46
%S 0,1,2,4,16,96,576,3368,20672,141760,1091200,9098112,79676928,
%T 726208640,6919738112,69344336896,731241201664,8076031881216,
%U 92856867250176,1106883171037184,13655807547883520,174298975125127168,2300708116863287296,31372716744306524160
%N Expansion of e.g.f. sinh(exp(x)*x).
%H Alois P. Heinz, <a href="/A009565/b009565.txt">Table of n, a(n) for n = 0..541</a>
%p a:= n-> add(`if`(k::odd, binomial(n, k)*k^(n-k), 0), k=0..n):
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Jan 15 2018
%t With[{nmax = 50}, CoefficientList[Series[Sinh[x*Exp[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jan 21 2018 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(sinh(x*exp(x))))) \\ _G. C. Greubel_, Jan 21 2018
%Y Cf. A009121.
%K nonn,easy
%O 0,3
%A _R. H. Hardin_
%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997
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