A352253 - OEIS

A352253

Expansion of e.g.f. 1 / (1 - x * sinh(x) / 2) (even powers only).

1, 1, 8, 153, 5492, 316625, 26774622, 3121729709, 479962730648, 94087054172673, 22904161764512570, 6778870099212235805, 2397161662661680925364, 998186321121004312238513, 483430830256916593106991782, 269435322393253822641626419725, 171224984800186115316322226731952

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..16.

FORMULA

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

MATHEMATICA

nmax = 32; Take[CoefficientList[Series[1/(1 - x Sinh[x]/2), {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}]

a[0] = 1; a[n_] := a[n] = Sum[Binomial[2 n, 2 k] k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]

PROG

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