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A357322 Expansion of e.g.f. -LambertW(log(1 - 3*x)/3). 2
0, 1, 5, 45, 586, 10024, 213084, 5428072, 161475320, 5501761488, 211466328400, 9057714349672, 428022643010544, 22127292215218072, 1242503403120434168, 75319473068729478360, 4902798528238919060224, 341102498012848479889408 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Lambert W-Function.

FORMULA

a(n) = Sum_{k=1..n} 3^(n-k) * k^(k-1) * |Stirling1(n,k)|.

a(n) ~ 3^(n - 1/2) * n^(n-1) / ((-1 + exp(3*exp(-1)))^(n - 1/2) * exp(n - 1/2 - 3*n*exp(-1))). - Vaclav Kotesovec, Oct 04 2022

MATHEMATICA

With[{m = 20}, Range[0, m]! * CoefficientList[Series[-ProductLog[Log[1 - 3*x]/3], {x, 0, m}], x]] (* Amiram Eldar, Sep 24 2022 *)

PROG

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(log(1-3*x)/3))))

(PARI) a(n) = sum(k=1, n, 3^(n-k)*k^(k-1)*abs(stirling(n, k, 1)));

CROSSREFS

Cf. A052807, A357321.

Sequence in context: A051539 A007696 A090136 * A090356 A201365 A112940

Adjacent sequences: A357319 A357320 A357321 * A357323 A357324 A357325

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Sep 24 2022

STATUS

approved

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Last modified November 29 10:31 EST 2022. Contains 358424 sequences. (Running on oeis4.)