A371121 E.g.f. satisfies A(x) = 1 - x*A(x)*log(1 - x*A(x)).

1, 0, 2, 3, 56, 330, 5724, 68460, 1351552, 24594192, 578257200, 13915923120, 389216689344, 11518744311360, 377576873670528, 13185760854520800, 497969104450867200, 19992393239486976000, 856421361373185137664, 38819358713756193292800

Offset: 0

Author

Seiichi Manyama, Mar 11 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370993, A371117, A371122.

Cf. A371119.

Programs

PARI

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

Formula

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

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