OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..568
FORMULA
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * (k+1) * a(n-2*k-1).
MATHEMATICA
nmax = 25; CoefficientList[Series[Exp[(Sinh[x] + x Cosh[x])/2], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 2 k] (k + 1) a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 25}]
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp((sinh(x) + x*cosh(x))/2))) \\ Michel Marcus, Feb 26 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 26 2022
STATUS
approved