A371138 E.g.f. satisfies A(x) = 1 - x^2*A(x)^2*log(1 - x*A(x)).

1, 0, 0, 6, 12, 40, 2340, 18648, 154560, 5767200, 95911200, 1438778880, 48014778240, 1228487644800, 27997623029376, 972327510000000, 32550437645107200, 1006902423902269440, 38894136241736494080, 1569697954634035537920, 61093442927846310912000

Offset: 0

Author

Seiichi Manyama, Mar 12 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370994, A371118.

Cf. A371121.

Programs

PARI

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

Formula

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

E.g.f.: (1/x) * Series_Reversion( x/(1 - x^2*log(1 - x)) ). - Seiichi Manyama, Sep 19 2024