A371147 E.g.f. satisfies A(x) = 1/(1 - x*A(x))^(x^2*A(x)^2).

1, 0, 0, 6, 12, 40, 2700, 21168, 173040, 7611840, 125415360, 1848591360, 71211998880, 1844075600640, 41500836336960, 1609925690419200, 55708371912211200, 1719475797882286080, 72091120665964654080, 3046645011228998860800, 119757727692451283097600

Offset: 0

Author

Seiichi Manyama, Mar 13 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A184949, A371145.

Programs

PARI

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n+1)^(k-1) * |Stirling1(n-2*k,k)|/(n-2*k)!.

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