A346390 E.g.f.: -log( 1 - (exp(x) - 1)^3 / 3! ).

1, 6, 25, 100, 511, 3626, 30045, 262800, 2470171, 25889446, 302003065, 3821936300, 51672723831, 745789322466, 11505096936085, 189023074558600, 3288243760145491, 60319276499454686, 1164282909466221105, 23603464830964817700, 501435697062735519151

Offset

3,2

Links

Table of n, a(n) for n=3..23.

Formula

a(n) = Stirling2(n,3) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling2(n-k,3) * k * a(k).

a(n) ~ (n-1)! / (log(6^(1/3)+1))^n. - Vaclav Kotesovec, Aug 09 2021

Mathematica

nmax = 23; CoefficientList[Series[-Log[1 - (Exp[x] - 1)^3/3!], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 3] &
a[n_] := a[n] = StirlingS2[n, 3] + (1/n) Sum[Binomial[n, k] StirlingS2[n - k, 3] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 3, 23}]

Prog

(PARI) my(x='x+O('x^25)); Vec(serlaplace(-log(1-(exp(x)-1)^3/3!))) \\ Michel Marcus, Aug 09 2021

Crossrefs

Cf. A000392, A000629, A003704, A327504, A346894, A346954, A346955.

Sequence in context: A034347 A009121 A327504 * A323824 A037537 A253220

Adjacent sequences: A346387 A346388 A346389 * A346391 A346392 A346393

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 08 2021

Status

approved