A349505 E.g.f. satisfies: A(x) = (1 + x)^(A(x)^3).

1, 1, 6, 81, 1668, 46740, 1659102, 71386602, 3611376360, 210083758704, 13817649943440, 1013979735381888, 82134894774767832, 7279520816638839600, 700730732176038359208, 72803537907677356262760, 8120227815636769492383168

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..n} (3*k+1)^(k-1) * Stirling1(n,k).

E.g.f. A(x) = Sum_{k>=0} (3*k+1)^(k-1) * (log(1+x))^k / k!.

From Vaclav Kotesovec, Nov 20 2021: (Start)

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

a(n) ~ n^(n-1) / (sqrt(3) * (exp(exp(-1)/3) - 1)^(n - 1/2) * exp(n + exp(-1)/6 - 5/6)). (End)

Mathematica

nmax = 20; CoefficientList[Series[(-LambertW[-3*Log[1 + x]]/(3*Log[1 + x]))^(1/3), {x, 0, nmax}], x]*Range[0, nmax]! (* Vaclav Kotesovec, Nov 20 2021 *)

Prog

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

Crossrefs

Cf. A008275, A033917, A264408, A349504, A349525.

Sequence in context: A197076 A234872 A064341 * A052756 A349651 A193265

Adjacent sequences: A349502 A349503 A349504 * A349506 A349507 A349508

Keyword

nonn

Author

Seiichi Manyama, Nov 20 2021

Status

approved