A357395 E.g.f. satisfies A(x) = exp(x * exp(3 * A(x))) - 1.

0, 1, 7, 109, 2677, 90226, 3873007, 202134997, 12427851625, 879806921041, 70486590597331, 6304879010400202, 622838214328334077, 67347956304168803173, 7911963620634266270071, 1003477119181096373029261, 136658009168055564212000209, 19889317400287888238121299854

Offset

0,3

Links

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

Index entries for reversions of series

Formula

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

a(n) ~ n^(n-1) / (3 * sqrt(1 + LambertW(1/3)) * LambertW(1/3)^n * exp(n*(4 - 1/LambertW(1/3)))). - Vaclav Kotesovec, Nov 14 2022

E.g.f.: Series_Reversion( exp(-3*x) * log(1 + x) ). - Seiichi Manyama, Sep 10 2024

Mathematica

Table[Sum[(3*n)^(k-1) * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 14 2022 *)

Prog

(PARI) a(n) = sum(k=1, n, (3*n)^(k-1)*stirling(n, k, 2));

Crossrefs

Cf. A052888, A357394.

Cf. A357336.

Sequence in context: A274787 A116875 A374882 * A371317 A303109 A101924

Adjacent sequences: A357392 A357393 A357394 * A357396 A357397 A357398

Keyword

nonn

Author

Seiichi Manyama, Sep 26 2022

Status

approved