A091756 Seventh column (m=8) of array A091752 ((-1,2)Stirling2).

1, 220, 48720, 14463680, 5762556800, 3000655257600, 1987324218880000, 1634736979972096000, 1636859558116823040000, 1961447726093804748800000, 2772502956616965206835200000, 4565871212782705024303104000000, 8667353356325850744087642112000000, 18789301668434870837372923150336000000

Offset: 4

Author

Wolfdieter Lang, Feb 27 2004

Keywords

• nonn
• easy
• changed

Crossrefs

Cf. A052502, A091752.

Programs

Mathematica

a[n_] := (9/6!)*(n-3)*(9*n^3 - 45*n^2 + 36*n + 40)*(3*(n-3))!/((3^(n-3))*(n-3)!); Array[a, 15, 4] (* Amiram Eldar, Aug 30 2025 *)

Formula

a(n) = A091752(n, 8), n>=4.

a(n) = (9/6!)*(n-3)*(9*n^3-45*n^2+36*n+40)*(3*(n-3))!/((3^(n-3))*(n-3)!) = (9/6!)*(n-3)*(9*n^3-45*n^2+36*n+40) * A052502(n-3), n>=4.

a(n) ~ 3^(2*n-7/2) * n^(2*n-2) /(80 * exp(2*n-12/n)). - Amiram Eldar, Aug 30 2025