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

0,3

Links

Table of n, a(n) for n=0..19.

Index entries for reversions of series

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

a(n) ~ (1 - (phi-1)*log(1 - 1/phi))^(n + 3/2) * n^(n-1) / (phi * sqrt(2*phi-1) * exp(n) * (phi - 1)^(n + 1/2)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Feb 03 2026

Mathematica

Table[n!^2 * Sum[Abs[StirlingS1[n-k, k]] / ((n-k)! * (n-k+1)!), {k, 0, n/2}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 03 2026 *)

Prog

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

Crossrefs

Cf. A370993, A371117, A371122.

Cf. A371119.

Sequence in context: A362835 A375688 A371140 * A371227 A179281 A000656

Adjacent sequences: A371118 A371119 A371120 * A371122 A371123 A371124

Keyword

nonn

Author

Seiichi Manyama, Mar 11 2024

Status

approved