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%I M4541 #21 Apr 11 2014 05:09:44
%S 1,0,-8,-56,64,12672,309376,2917888,-163782656,-12716052480,
%T -495644917760,-4004259037184,1359174582304768,153146435763437568,
%U 9620207941273255936,142966118908253962240,-62984506636368191946752
%N E.g.f. sin(sinh(x)) (odd powers only).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A003722/b003722.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = sum(j=1..n+1, (sum(i=0..2*j-1, (-1)^(i+j-1)*(2*j-1-2*i)^(2*n+1)*binomial(2*j-1,i)))/(2^(2*j-1)*(2*j-1)!)); [_Vladimir Kruchinin_, Jun 09 2011]
%t With[{nn = 50}, Take[CoefficientList[Series[Sin[Sinh[x]], {x, 0, nn}], x] Range[0, nn - 1]!, {2, -1, 2}]] (* _Vincenzo Librandi_, Apr 11 2014 *)
%o (Maxima)
%o a(n):=sum((sum((-1)^(i+j-1)*(2*j-1-2*i)^(2*n+1)*binomial(2*j-1,i),i,0,2*j-1))/(2^(2*j-1)*(2*j-1)!),j,1,n+1); /* _Vladimir Kruchinin_, Jun 09 2011 */
%K sign
%O 0,3
%A _R. H. Hardin_, _Simon Plouffe_
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