A367166 E.g.f. satisfies A(x) = 1 + A(x)^3 * (1 - exp(-x*A(x))).

1, 1, 7, 106, 2493, 79866, 3245591, 159980122, 9275436505, 618568035130, 46649552389515, 3925749706207770, 364709764578733349, 37075283015959294666, 4093764536232959203999, 487906508897555966553370, 62428514041971948893889969, 8535465441907344876112112346

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * (n+3*k)!/(n+2*k+1)! * Stirling2(n,k).

Prog

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

Crossrefs

Cf. A367165.

Sequence in context: A360370 A203971 A145167 * A141358 A141362 A213863

Adjacent sequences: A367163 A367164 A367165 * A367167 A367168 A367169

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2023

Status

approved