A357394 E.g.f. satisfies A(x) = exp(x * exp(2 * A(x))) - 1.
0, 1, 5, 55, 953, 22651, 685525, 25222359, 1093148145, 54549313651, 3080446982221, 194213549023407, 13522789698386281, 1030619149263349387, 85336828127587240261, 7628421633465044832391, 732208108150442899232737, 75108533335473988089786147
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[(2*n)^(k-1) * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 14 2022 *) -
PARI
a(n) = sum(k=1, n, (2*n)^(k-1)*stirling(n, k, 2));
Formula
a(n) = Sum_{k=1..n} (2 * n)^(k-1) * Stirling2(n,k).
a(n) ~ n^(n-1) / (2 * sqrt(1 + LambertW(1/2)) * LambertW(1/2)^n * exp(n*(3 - 1/LambertW(1/2)))). - Vaclav Kotesovec, Nov 14 2022
E.g.f.: Series_Reversion( exp(-2*x) * log(1 + x) ). - Seiichi Manyama, Sep 10 2024