A352251 Expansion of e.g.f. 1 / (1 - x * sinh(x)) (even powers only).

1, 2, 28, 966, 62280, 6452650, 980531916, 205438870014, 56760128400016, 19994672935658322, 8746764024725937300, 4651991306703670964518, 2956156902003429777549144, 2212026607642404922284728826, 1925137044528752884360406444380, 1928103808741894922401976601295950

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(2*n,2*k) * k * a(n-k).

Mathematica

nmax = 30; Take[CoefficientList[Series[1/(1 - x Sinh[x]), {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}]
a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[2 n, 2 k] k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]

Prog

(PARI) my(x='x+O('x^40), v=Vec(serlaplace(1 /(1-x*sinh(x))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Mar 10 2022

Crossrefs

Cf. A006153, A006154, A009233, A094088, A205571, A210672, A351762, A352250, A352252, A352253.

Sequence in context: A009256 A012725 A264637 * A012756 A362587 A009403

Adjacent sequences: A352248 A352249 A352250 * A352252 A352253 A352254

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 09 2022

Status

approved