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A346894 E.g.f.: 1 / (1 - (exp(x) - 1)^3 / 3!). 3
1, 0, 0, 1, 6, 25, 110, 721, 6286, 57625, 541470, 5558641, 64351166, 819480025, 11140978030, 160711583761, 2472834185646, 40597082635225, 706816137889790, 12974021811748081, 250395124862965726, 5074637684604691225, 107798916619788396750 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * Stirling2(k,3) * a(n-k).

a(n) ~ n! / (3*(1 + 6^(-1/3)) * log(1 + 6^(1/3))^(n+1)). - Vaclav Kotesovec, Aug 08 2021

MATHEMATICA

nmax = 22; CoefficientList[Series[1/(1 - (Exp[x] - 1)^3/3!), {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] StirlingS2[k, 3] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]

PROG

(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-(exp(x)-1)^3/3!))) \\ Michel Marcus, Aug 06 2021

CROSSREFS

Cf. A000392, A000670, A327504, A330047, A346895.

Sequence in context: A212258 A048875 A295202 * A094669 A100296 A346818

Adjacent sequences:  A346891 A346892 A346893 * A346895 A346896 A346897

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 06 2021

STATUS

approved

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Last modified October 26 05:34 EDT 2021. Contains 348256 sequences. (Running on oeis4.)