A067454 Binomial(a,b) where a = n! and b = sum of first n natural numbers.

1, 1, 0, 1, 1961256, 4730523156632595024, 14714642085645788453359573419196194379200, 141671570521482692258866117076218807527442238234361038404229857860891009480

Offset: 0

Author

Amarnath Murthy, Feb 05 2002

Keywords

• easy
• nonn

Comments

Terms from Robert G. Wilson v.

Crossrefs

Cf. A067454, A086687.

Programs

Mathematica

Table[Binomial[n!, n(n + 1)/2], {n, 0, 8}] (* Robert G. Wilson v *)

Formula

From Vaclav Kotesovec, May 29 2025: (Start)

a(n) ~ n!^(n*(n+1)/2) / (n*(n+1)/2)!.

a(n) ~ 2^(3*n^2/4 + 3*n/4) * Pi^(n^2/4 + n/4 - 1/2) * n^(n^3/2 - n^2/4 - 3*n/4 - 1) / exp(n^3/2 - n/24 + 5/24). (End)