A392954 E.g.f. A(x) satisfies A(x) = 1 + (A(x)/x) * (exp(x^2*A(x)) - 1).

1, 1, 4, 33, 396, 6320, 126540, 3052770, 86259600, 2795449104, 102237851520, 4166113145040, 187198818871680, 9196061105705760, 490339254174850080, 28204673605838730000, 1740913974945559814400, 114779720686270595155200, 8050595846752949415045120

Offset

0,3

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (2*n-3*k)!/(n-k+1)! * Stirling2(n-k,n-2*k)/(n-k)!.

Mathematica

Table[n!* Sum[(2*n-3*k)!/(n-k+1)!*Abs[StirlingS2[n-k, n-2*k]/(n-k)!], {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vincenzo Librandi, Jan 28 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (2*n-3*k)!/(n-k+1)!*stirling(n-k, n-2*k, 2)/(n-k)!);
(Magma) [Factorial(n)* &+[Factorial(2*n-3*k) / Factorial(n-k+1) * Abs(StirlingSecond(n-k, n-2*k)) /Factorial(n-k): k in [0..Floor(n/2)] ] : n in [0..23] ]; // Vincenzo Librandi, Jan 28 2026

Crossrefs

Cf. A392930.

Sequence in context: A293193 A295256 A269926 * A392930 A331794 A156132

Adjacent sequences: A392951 A392952 A392953 * A392955 A392956 A392957

Keyword

nonn,changed

Author

Seiichi Manyama, Jan 28 2026

Status

approved