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A321192
a(n) = [x^n] Product_{k>=1} (1 + x^k)^tau_n(k), where tau_n(k) = number of ordered n-factorizations of k.
3
1, 1, 2, 6, 20, 55, 239, 700, 3212, 10104, 48622, 161579, 806843, 2799199, 14379647, 52018828, 273472712, 1023655306, 5491615463, 21234676241, 115910309103, 460998296937, 2556361045845, 10440651927427, 58714921974979, 245586789818255, 1399187406060485
OFFSET
0,3
LINKS
FORMULA
a(n) = [x^n] Product_{k_1>=1, k_2>=1, ..., k_n>=1} (1 + x^(k_1*k_2*...*k_n)).
MATHEMATICA
tau[n_, 1] = 1; tau[n_, k_] := tau[n, k] = Plus @@ (tau[#, k-1] & /@ Divisors[n]); nmax = 30; Table[SeriesCoefficient[Product[(1 + x^k)^tau[k, n], {k, 1, n}], {x, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, Oct 29 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 29 2018
STATUS
approved