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A305867
Expansion of Product_{k>=1} 1/(1 - x^k)^(2*k-1)!!.
3
1, 1, 4, 19, 130, 1120, 11960, 151595, 2230550, 37361755, 701873371, 14610774346, 333746628499, 8298025724194, 223049950124065, 6444634486214748, 199165237980655863, 6555102341516877027, 228905611339161301812, 8452656930719845696590, 329075775511339959533232, 13471099892869946627980017
OFFSET
0,3
COMMENTS
Euler transform of A001147.
LINKS
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}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 12 2018
STATUS
approved