A371119 - OEIS

A371119

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

1, 0, 2, 3, 52, 305, 4866, 57337, 1048776, 18547713, 407900710, 9436057961, 248501026236, 7021087254337, 217488458525898, 7223642070331065, 258233053457437456, 9841074705853124609, 399304906991091898830, 17163110041947804495817, 779646387683354742170820

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

Index entries for reversions of series

FORMULA

a(n) = (n!)^2 * Sum_{k=0..floor(n/2)} Stirling2(n-k,k)/( (n-k)! * (n-k+1)! ).

E.g.f.: (1/x) * Series_Reversion( x/(1 + x*(exp(x) - 1)) ). - Seiichi Manyama, Sep 19 2024

PROG

(PARI) a(n) = n!^2*sum(k=0, n\2, stirling(n-k, k, 2)/((n-k)!*(n-k+1)!));

CROSSREFS