A389002 Expansion of e.g.f. (1/6) * ( log(1 + x) / (1 - x) )^3.

1, 6, 65, 525, 5719, 57764, 707048, 8560140, 119098716, 1680123720, 26407385784, 425277530496, 7479730381824, 135390234989952, 2639566562179968, 53047516141728000, 1136684203107252480, 25112909339835056640, 587014131059100587520, 14140770438737046804480, 358231630643999780198400, 9344721317125085340364800

Offset

3,2

Links

Table of n, a(n) for n=3..24.

Formula

a(n) = (1/2) * Sum_{k=0..n} binomial(n,k) * Stirling1(k,3) * (n-k+2)!.

a(n) ~ log(2)^3 * n^2 * n! / 12. - Vaclav Kotesovec, Sep 22 2025

Mathematica

nmax = 24; CoefficientList[Series[(1/6) (Log[1 + x]/(1 - x))^3, {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 3] &
Table[(1/2) Sum[Binomial[n, k] StirlingS1[k, 3] (n - k + 2)!, {k, 0, n}], {n, 3, 24}]

Crossrefs

Cf. A000399, A001713, A024167, A389001, A389003.

Sequence in context: A179879 A350946 A297516 * A099343 A189509 A360977

Adjacent sequences: A388999 A389000 A389001 * A389003 A389004 A389005

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 22 2025

Status

approved