A357349 E.g.f. satisfies A(x) = log(1 + x * exp(A(x))) * exp(A(x)).

0, 1, 3, 23, 278, 4624, 98064, 2530142, 76931224, 2694025872, 106782582720, 4726084696992, 231030209532528, 12362764041338736, 718779255989466840, 45118706229328822680, 3041140847160686156544, 219071239142209684437504, 16796070771249534388114176

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..359

Index entries for reversions of series

Formula

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

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

a(n) ~ (exp(s) + s - 1)^n * n^(n-1) / (sqrt(3 - 2*s - (1-s)^2/exp(s)) * exp((1-s)*n) * (1-s)^(n - 1/2)), where s = 0.53817220326839364060187876447947735356697317... is the root of the equation s = exp(s) * (s - log(exp(s) + s - 1)) . - Vaclav Kotesovec, Jan 24 2026

Mathematica

Table[Sum[(n+k)^(k-1) * StirlingS1[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 24 2026 *)

Prog

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

Crossrefs

Cf. A357350, A357351, A357423.

Cf. A162655.

Sequence in context: A302117 A343772 A006555 * A383316 A363137 A060090

Adjacent sequences: A357346 A357347 A357348 * A357350 A357351 A357352

Keyword

nonn

Author

Seiichi Manyama, Sep 25 2022

Status

approved