A371145 E.g.f. satisfies log(A(x)) = x^2*A(x)^2 * (exp(x*A(x)) - 1).

1, 0, 0, 6, 12, 20, 2550, 20202, 105896, 6501672, 111489930, 1203491630, 53987127612, 1496864088876, 27032265220142, 1088916434686290, 40758246253626960, 1081683296597292752, 44159293393817257746, 1998309768008640244182, 71124972575776526592740

Offset

0,4

Links

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

Index entries for reversions of series

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n+1)^(k-1) * Stirling2(n-2*k,k)/(n-2*k)!.

E.g.f.: (1/x) * Series_Reversion( x*exp(x^2*(1 - exp(x))) ). - Seiichi Manyama, Sep 21 2024

Prog

(PARI) a(n) = n!*sum(k=0, n\3, (n+1)^(k-1)*stirling(n-2*k, k, 2)/(n-2*k)!);

Crossrefs

Cf. A356785.

Sequence in context: A371304 A355508 A371139 * A370989 A055458 A360570

Adjacent sequences: A371142 A371143 A371144 * A371146 A371147 A371148

Keyword

nonn

Author

Seiichi Manyama, Mar 13 2024

Status

approved