A346955 E.g.f.: -log( 1 - (exp(x) - 1)^5 / 5! ).

1, 15, 140, 1050, 6951, 42651, 253660, 1594230, 12463451, 134921787, 1806513072, 25539589530, 355175465191, 4797717669123, 63797550625676, 860468790181686, 12275324511112971, 192498455326842819, 3353266112959628272, 63379650000684213834

Offset

5,2

Links

Table of n, a(n) for n=5..24.

Formula

a(n) = Stirling2(n,5) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling2(n-k,5) * k * a(k).

a(n) ~ (n-1)! / (log(120^(1/5) + 1))^n. - Vaclav Kotesovec, Aug 09 2021

Mathematica

nmax = 24; CoefficientList[Series[-Log[1 - (Exp[x] - 1)^5/5!], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 5] &
a[n_] := a[n] = StirlingS2[n, 5] + (1/n) Sum[Binomial[n, k] StirlingS2[n - k, 5] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 5, 24}]

Crossrefs

Cf. A000481, A000629, A003704, A327506, A346390, A346920, A346954.

Sequence in context: A000481 A365528 A327506 * A346920 A215765 A055903

Adjacent sequences: A346952 A346953 A346954 * A346956 A346957 A346958

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 08 2021

Status

approved