A371269 E.g.f. satisfies A(x) = 1 + x*A(x) * (exp(x*A(x)^2) - 1).

1, 0, 2, 3, 76, 485, 10746, 146167, 3552312, 75642345, 2150551990, 61400333291, 2061654862356, 72804918721405, 2858153637295698, 119363732105632575, 5395737275060765296, 259270058379207421649, 13294348104095211012462, 721446934706871966578899

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

Prog

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

Crossrefs

Cf. A371262, A371270, A371271.

Cf. A371228.

Sequence in context: A176290 A371143 A370988 * A306195 A091825 A166091

Adjacent sequences: A371266 A371267 A371268 * A371270 A371271 A371272

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2024

Status

approved