A091031 Third to last entries in rows of array A090452 (scaled (3,2)-Stirling2).

1, 16, 114, 644, 3270, 15642, 72072, 323752, 1428102, 6214520, 26761196, 114287736, 484816540, 2045277990, 8588492100, 35923392720, 149753379270, 622458753840, 2580709189740, 10675646755800, 44074384410420, 181638630107220, 747375951913344, 3070765657798704

Offset: 2

Author

Wolfdieter Lang, Jan 09 2004

Keywords

• nonn
• easy
• changed

Crossrefs

Cf. A000108 (last row entries), 3*A002054(n-1) (second to last row entries), A000108, A090452.

Programs

Mathematica

a[n_] := (9*n^2 - 19*n + 8)*(n-1) * CatalanNumber[n]/(4*(2*n-1)); Array[a, 25, 2] (* Amiram Eldar, Aug 30 2025 *)

Formula

a(n) = A090452(n, 2*(n-1)), n>=2.

a(n) = (9*n^2-19*n+8)*(n-1)*C(n)/(4*(2*n-1)), n>=2; with the Catalan numbers C(n) = A000108(n).

a(n) ~ 9 * 2^(2*n-3) * sqrt(n/Pi). - Amiram Eldar, Aug 30 2025