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%I #21 Jun 30 2022 03:34:32
%S 1,1,2,10,56,376,3152,30640,338816,4226176,58564352,892337920,
%T 14834994176,267186021376,5182147684352,107689460377600,
%U 2387077442011136,56219583797886976,1401949974947889152,36902741817196871680,1022494706646806429696
%N Expansion of e.g.f. 1/(1 - sinh(x)*cosh(x)).
%H Seiichi Manyama, <a href="/A191277/b191277.txt">Table of n, a(n) for n = 0..427</a>
%F a(n) = Sum_{k=1..n} Sum_{i=0..k} (-1)^i*(k-2*i)^n*binomial(k,i), n>0, a(0)=1.
%F a(n) ~ n! /(sqrt(5)*(log(2+sqrt(5))/2)^(n+1)). - _Vaclav Kotesovec_, Jun 26 2013
%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * binomial(n,2*k+1) * a(n-2*k-1). - _Seiichi Manyama_, Jun 30 2022
%t CoefficientList[Series[1/(1-Sinh[x]*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 26 2013 *)
%o (Maxima) a(n):=sum(sum((-1)^i*(k-2*i)^n*binomial(k,i),i,0,k),k,1,n);
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(1/(1 - sinh(x)*cosh(x)))) \\ _Michel Marcus_, Jun 30 2022
%Y Cf. A006154, A009229.
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, May 29 2011
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