A086687 a(n) = binomial(n!,n).

1, 1, 1, 20, 10626, 190578024, 189492294437160, 16321981448897949868560, 173117930575796585984663510371920, 300649979042426162195454856425990347600496000, 109109335363647915965076917082046041529603540914857910625920

Offset: 0

Author

Jon Perry, Jul 28 2003

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..30
• Harlan J. Brothers, Pascal's triangle, Sidi polynomials, and powers of e, Missouri J. Math. Sci. (2025) Vol. 37, No. 1, 67-78.

Crossrefs

Cf. A036740.

Main diagonal of A180397.

Programs

Mathematica

Table[Binomial[n!,n],{n,0,12}] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2011*)

PARI

for(i=1,10,print1(","binomial(i!,i)))

Formula

From Vaclav Kotesovec, Jul 02 2016: (Start)

a(n) ~ (n!)^(n-1).

a(n) ~ 2^((n-1)/2) * Pi^((n-1)/2) * n^((2*n+1)*(n-1)/2) / exp(n^2-n-1/12).

(End)

Extensions

a(0)=1 prepended by Alois P. Heinz, Nov 06 2016