A331336 L.g.f.: log(Sum_{k>=0} k! * x^k / Product_{j=1..k} (1 - x^j)).

1, 5, 19, 97, 571, 4109, 33643, 310321, 3167101, 35427605, 430918489, 5663534761, 79999275253, 1208843786897, 19460746819099, 332560305456673, 6012905371554295, 114689550634547009, 2301617124055928731, 48479953395028134577, 1069433968820519576377

Offset: 1

Author

Ilya Gutkovskiy, Jan 14 2020

Keywords

• nonn

Crossrefs

Cf. A000203, A101880.

Programs

Mathematica

nmax = 21; CoefficientList[Series[Log[Sum[k! x^k/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest

Formula

exp(Sum_{n>=1} a(n) * x^n / n) = g.f. of A101880.

a(n) = n * A101880(n) - Sum_{k=1..n-1} A101880(k) * a(n-k).

a(n) ~ n * n! * (1 - 1/n^2 - 6/n^3 - 38/n^4 - 276/n^5 - 2354/n^6 - 23458/n^7 - 268991/n^8 - 3490842/n^9 - 50520252/n^10 - ...). - Vaclav Kotesovec, Jan 28 2020