A331335 L.g.f.: log(Sum_{k>=0} k! * x^k / Product_{j=1..k} (1 - j*x)).

1, 5, 31, 241, 2231, 23825, 287687, 3872961, 57514423, 934197425, 16480953127, 313919262625, 6422468800151, 140496324183185, 3273117681693191, 80916019512168321, 2115854823935820151, 58351931794643315825, 1692782510862560536807, 51533053881743794186081

Offset: 1

Author

Ilya Gutkovskiy, Jan 14 2020

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000670, A205543.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Log[Sum[k! x^k/Product[1 - j x, {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 A000670.

a(n) = n * A000670(n) - Sum_{k=1..n-1} A000670(k) * a(n-k).

a(n) ~ n * n! / (2 * (log(2))^(n+1)). - Vaclav Kotesovec, Jan 28 2020