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

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..427

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

Mathematica

CoefficientList[Series[1/(1-Sinh[x]*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

Prog

(Maxima) a(n):=sum(sum((-1)^i*(k-2*i)^n*binomial(k, i), i, 0, k), k, 1, n);
(PARI) my(x='x+O('x^30)); Vec(serlaplace(1/(1 - sinh(x)*cosh(x)))) \\ Michel Marcus, Jun 30 2022

Crossrefs

Cf. A006154, A009229.

Sequence in context: A243644 A000172 A097971 * A290443 A336961 A265954

Adjacent sequences: A191274 A191275 A191276 * A191278 A191279 A191280

Keyword

nonn

Author

Vladimir Kruchinin, May 29 2011

Status

approved