OFFSET
0,3
FORMULA
a(0) = 1; a(n) = (1/n) * Sum_{k=0..floor((n-1)/2)} (binomial(n,2*k+1) * (2*k+1)!)^2 * a(n-2*k-1) / (2*k+1).
MATHEMATICA
nmax = 18; CoefficientList[Series[Exp[Sum[x^(2 k + 1)/(2 k + 1)^2, {k, 0, Infinity}]], {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 1; a[n_] := a[n] = (1/n) Sum[(Binomial[n, 2 k + 1] (2 k + 1)!)^2 a[n - 2 k - 1]/(2 k + 1), {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 14 2021
STATUS
approved