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%I M4571 #29 Oct 02 2021 07:57:09
%S 1,0,-8,112,-128,-109824,8141824,-353878016,-9666461696,5151942574080,
%T -825073851170816,76429076694827008,2051308253366714368,
%U -2361338488910424047616,171581865952588387581952
%N Expansion of e.g.f. tan(tanh(x)) (odd powers only).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A003721/b003721.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = Sum_{i=0..(n-1)} ( ( Sum_{j=1..2*i+1} j!*2^(2*i+1-j-1)*(-1)^(i+j+1)*Stirling2(2*i+1,j) ) * Sum_{k=2*i+1..2*n-1} binomial(k-1,2*i)*k!*(-1)^(1+k)*2^(2*n-k-1)*Stirling2(2*n-1,k) )/(2*i+1)!. - _Vladimir Kruchinin_, Jun 10 2011
%t With[{nn=30},Take[CoefficientList[Series[Tan[Tanh[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Nov 05 2011 *)
%o (Maxima)
%o a(n):=sum(((sum(j!*2^(2*i+1-j-1)*(-1)^(i+j+1)*stirling2(2*i+1,j),j,1,2*i+1))*sum(binomial(k-1,2*i)*k!*(-1)^(1+k)*2^(2*n-k-1)*stirling2(2*n-1,k),k,2*i+1,2*n-1))/(2*i+1)!,i,0,(n-1)); /* _Vladimir Kruchinin_, Jun 10 2011 */
%Y Cf. A003716, A003718.
%K sign
%O 0,3
%A _R. H. Hardin_, _Simon Plouffe_
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