A306946 Expansion of e.g.f. Product_{k>=1} 1/(1 - x^(k^2)/k^2).
1, 1, 2, 6, 30, 150, 900, 6300, 52920, 516600, 5166000, 56826000, 689396400, 9135126000, 127891764000, 1918376460000, 32083427376000, 547888316976000, 9941031356256000, 188879595768864000, 3817981890122400000, 80266319244951840000, 1769328161437636800000
Offset: 0
Keywords
Programs
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Mathematica
nmax = 22; CoefficientList[Series[Product[1/(1 - x^k^2/k^2), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! nmax = 22; CoefficientList[Series[Exp[Sum[Sum[Boole[IntegerQ[d^(1/2)]] d^(1 - k/d), {d, Divisors[k]}] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[Sum[Boole[IntegerQ[d^(1/2)]] d^(1 - k/d), {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 22}]
Formula
a(n) ~ 2 * n!. - Vaclav Kotesovec, Mar 18 2019