A357338 E.g.f. satisfies A(x) = log(1 + x) * exp(3 * A(x)).

0, 1, 5, 65, 1302, 35904, 1260372, 53796168, 2704942440, 156602951568, 10260496538640, 750563024381928, 60636437884772208, 5362045857366832152, 515154874732515894744, 53432840588453561773080, 5950904875941534263739648, 708296073287989866587094528

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..336

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

Formula

E.g.f.: -LambertW(-3 * log(1 + x))/3.

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

a(n) ~ n^(n-1) / (sqrt(3) * (exp(exp(-1)/3) - 1)^(n - 1/2) * exp(n - 1/2 + exp(-1)/6)). - Vaclav Kotesovec, Oct 04 2022

Mathematica

nmax = 20; A[_] = 0;
Do[A[x_] = Log[1 + x]*Exp[3*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 05 2024 *)

Prog

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

Crossrefs

Cf. A277489, A357337.

Cf. A349505.

Sequence in context: A349517 A121822 A056245 * A195886 A079482 A147625

Adjacent sequences: A357335 A357336 A357337 * A357339 A357340 A357341

Keyword

nonn

Author

Seiichi Manyama, Sep 24 2022

Status

approved