A377390 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - x*log(1-x))^2 ).

1, 0, 4, 6, 232, 1380, 46308, 593880, 20639456, 434113344, 16557009840, 490894572960, 20995513516800, 801146038080960, 38632110899469696, 1791609186067646400, 97167945389675212800, 5275541489312858803200, 319879838094553691744256, 19820894989178283188198400

Offset: 0

Author

Seiichi Manyama, Oct 27 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A371121, A377391.

Cf. A371229, A377360.

Programs

PARI

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

Formula

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371229.

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