A319104 Expansion of e.g.f. Product_{k>=1} 1/(1 - x^(k^2))^(1/k^2).

1, 1, 2, 6, 30, 150, 900, 6300, 56700, 550620, 5506200, 60568200, 782951400, 10351341000, 144918774000, 2173781610000, 38080340298000, 653540914026000, 12158944705908000, 231019949412252000, 4855314209005260000, 102626845031971260000, 2275136280946849320000, 52328134461777534360000

Offset: 0

Author

Ilya Gutkovskiy, Sep 10 2018

Keywords

• nonn

Crossrefs

Cf. A001156, A028342, A046951.

Programs

Maple

seq(n!*coeff(series(mul(1/(1-x^(k^2))^(1/k^2),k=1..100),x=0,24),x,n),n=0..23); # Paolo P. Lava, Jan 09 2019

Mathematica

nmax = 23; CoefficientList[Series[Product[1/(1 - x^k^2)^(1/k^2), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Exp[Sum[Length[Select[Divisors[k], IntegerQ[Sqrt[#]] &]] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = (n - 1)! Sum[Length[Select[Divisors[k], IntegerQ[Sqrt[#]] &]] a[n - k]/(n - k)!, {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

Formula

E.g.f.: exp(Sum_{k>=1} A046951(k)*x^k/k).