A377330 E.g.f. satisfies A(x) = 1 + A(x)^2 * (exp(x*A(x)^2) - 1).

1, 1, 9, 163, 4537, 171451, 8206517, 476071275, 32469361617, 2546397256651, 225784275815485, 22336278201427675, 2439097416667718297, 291422424985108052091, 37817207428965579915333, 5296739332085114983427083, 796419825874139713780172449, 127955324543685857975407200235

Offset

0,3

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A052750, A367134, A367180.

Sequence in context: A041147 A041144 A212334 * A354900 A354892 A377329

Adjacent sequences: A377327 A377328 A377329 * A377331 A377332 A377333

Keyword

nonn

Author

Seiichi Manyama, Oct 25 2024

Status

approved