A367369 a(n) = A340556(2*n, n), the central terms of the second order Eulerian numbers.

1, 1, 22, 1452, 195800, 44765000, 15548960784, 7634832149392, 5036317938475648, 4297211671488276816, 4605775111899791292320, 6058134671618508819536768, 9595073255473201184093573376, 18012849924775292436074080925056, 39551575929026035832580350736305920

Offset: 0

Author

Peter Luschny, Nov 16 2023

Keywords

• nonn

Crossrefs

Indexing the second-order Eulerian numbers comes in three flavors: A008517 (following Riordan and Comtet), A201637 (following Graham, Knuth, and Patashnik) and indexing like in A340556 using the definition of Gessel and Stanley.

Programs

Maple

A340556 := (n, k) -> `if`(k=0, k^n, combinat:-eulerian2(n, k-1)):
seq(A340556(2*n, n), n = 0..14);

Mathematica

(* Using function T[n_, k_] from A340556. *)
Table[T[2 k, k], {k, 0, 14}] (* Shenghui Yang, Mar 07 2025 *)

SageMath

# Using function E2(n, k) from A340556.
print([E2(2*n, n) for n in (0..14)])  # Peter Luschny, Mar 07 2025