A371119 E.g.f. satisfies A(x) = 1 + x*A(x)*(exp(x*A(x)) - 1).

1, 0, 2, 3, 52, 305, 4866, 57337, 1048776, 18547713, 407900710, 9436057961, 248501026236, 7021087254337, 217488458525898, 7223642070331065, 258233053457437456, 9841074705853124609, 399304906991091898830, 17163110041947804495817, 779646387683354742170820

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

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

Crossrefs

Cf. A370988, A371115, A371120.

Cf. A371121.

Sequence in context: A362836 A371142 A337057 * A371262 A193332 A192182

Adjacent sequences: A371116 A371117 A371118 * A371120 A371121 A371122

Keyword

nonn

Author

Seiichi Manyama, Mar 11 2024

Status

approved