A371302 E.g.f. satisfies A(x) = 1/(1 + x^2*log(1 - x*A(x))).

1, 0, 0, 6, 12, 40, 1620, 13608, 117600, 2924640, 49603680, 782147520, 19083936960, 463369645440, 10836652514688, 304533583200000, 9218842256332800, 281872333420554240, 9421579421176089600, 338543319734116116480, 12590519274541116518400

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-k)! * |Stirling1(n-2*k,k)|/( (n-2*k)! * (n-2*k+1)! ).

Mathematica

Table[n!*Sum[(n-k)!* Abs[StirlingS1[n-2*k, k]]/((n-2*k)!*(n-2*k+1)!), {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Feb 25 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, (n-k)!*abs(stirling(n-2*k, k, 1))/((n-2*k)!*(n-2*k+1)!));
(Magma) [Factorial(n)* &+[Factorial(n-k)*Abs(StirlingFirst(n-2*k, k)) /( Factorial(n-2*k) * Factorial(n-2*k+1) ): k in [0..Floor(n/3)] ] : n in [0..23] ]; // Vincenzo Librandi, Feb 25 2026

Crossrefs

Cf. A370994, A371118, A371138.

Cf. A351503.

Sequence in context: A355287 A375826 A362891 * A371233 A356970 A371138

Adjacent sequences: A371299 A371300 A371301 * A371303 A371304 A371305

Keyword

nonn

Author

Seiichi Manyama, Mar 18 2024

Status

approved