A367165 E.g.f. satisfies A(x) = 1 + A(x)^2 * (1 - exp(-x*A(x))).

1, 1, 5, 52, 835, 18216, 503349, 16855084, 663482831, 30028551760, 1536446339593, 87704127028068, 5525854843477995, 380920533712670056, 28518416931490444157, 2304386381189483726044, 199888539403801152219271, 18526504345764539763792576

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * (n+2*k)!/(n+k+1)! * Stirling2(n,k).

Prog

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

Crossrefs

Cf. A367166.

Sequence in context: A280063 A363356 A365012 * A357346 A196531 A108459

Adjacent sequences: A367162 A367163 A367164 * A367166 A367167 A367168

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2023

Status

approved