A364942 E.g.f. satisfies A(x) = exp( x*A(x)^2 / (1 - x*A(x))^3 ).

1, 1, 11, 193, 5037, 176221, 7755433, 411995529, 25665442841, 1835264297881, 148192928581581, 13338664928207389, 1324344628799752981, 143792046846092303829, 16949599953405295395521, 2155710634160924802161041, 294250014166281073851809457

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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

Prog

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

Crossrefs

Cf. A361142, A364941.

Sequence in context: A258295 A213691 A112127 * A142996 A201185 A345342

Adjacent sequences: A364939 A364940 A364941 * A364943 A364944 A364945

Keyword

nonn

Author

Seiichi Manyama, Aug 14 2023

Status

approved