OFFSET
0,3
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n-1,2*k-1) * k * a(n-k).
MATHEMATICA
nmax = 36; Take[CoefficientList[Series[Exp[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 - 1, 2 k - 1] k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
PROG
(PARI) my(x='x+O('x^40), v=Vec(serlaplace(exp(x*sinh(x)/2)))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Mar 10 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 09 2022
STATUS
approved