A191277 Expansion of e.g.f. 1/(1 - sinh(x)*cosh(x)).
1, 1, 2, 10, 56, 376, 3152, 30640, 338816, 4226176, 58564352, 892337920, 14834994176, 267186021376, 5182147684352, 107689460377600, 2387077442011136, 56219583797886976, 1401949974947889152, 36902741817196871680, 1022494706646806429696
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..427
Programs
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Mathematica
CoefficientList[Series[1/(1-Sinh[x]*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *) -
Maxima
a(n):=sum(sum((-1)^i*(k-2*i)^n*binomial(k,i),i,0,k),k,1,n);
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PARI
my(x='x+O('x^30)); Vec(serlaplace(1/(1 - sinh(x)*cosh(x)))) \\ Michel Marcus, Jun 30 2022
Formula
a(n) = Sum_{k=1..n} Sum_{i=0..k} (-1)^i*(k-2*i)^n*binomial(k,i), n>0, a(0)=1.
a(n) ~ n! /(sqrt(5)*(log(2+sqrt(5))/2)^(n+1)). - Vaclav Kotesovec, Jun 26 2013
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