A265950 Expansion of Product_{k>=1} (1 + k!*x^k).

1, 1, 2, 8, 30, 156, 900, 6192, 47904, 422928, 4138848, 44864640, 531227520, 6836927040, 94891046400, 1413494219520, 22481104677120, 380261238681600, 6814832064422400, 128991143627965440, 2571187988206540800, 53834676521793638400, 1181214133296983654400

Offset: 0

Author

Vaclav Kotesovec, Dec 19 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..440

Crossrefs

Cf. A077365, A265954.

Programs

Mathematica

nmax=30; CoefficientList[Series[Product[(1+k!*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ n! * (1 + 1/n + 2/n^2 + 10/n^3 + 56/n^4 + 394/n^5 + 3332/n^6 + 32782/n^7 + 368072/n^8 + 4651666/n^9 + 65440748/n^10 + ...), for coefficients see A265954.

G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*(j!)^k*x^(j*k)/k). - Ilya Gutkovskiy, Jun 18 2018