OFFSET
0,3
COMMENTS
Euler transform of A001147.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..404
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Double Factorial
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^A001147(k).
MAPLE
N:= 25:
S:=series(mul((1-x^k)^(-doublefactorial(2*k-1)), k=1..N), x, N+1):
seq(coeff(S, x, n), n=0..N); # Robert Israel, Jun 12 2018
MATHEMATICA
nmax = 21; CoefficientList[Series[Product[1/(1 - x^k)^(2 k - 1)!!, {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (2 d - 1)!!, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 21}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 12 2018
STATUS
approved