A052140 a(n) = 4^n * n!^2 * Sum_{k=0..n} 1/k!.

1, 8, 160, 6144, 399360, 40058880, 5771427840, 1131282432000, 289610945003520, 93834041307955200, 37533620328254668800, 18166272406298453606400, 10463772914064222584832000, 7073510490325302759338803200, 5545632224438439107673194496000, 4991069001995999301566969413632000

Offset

0,2

References

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.64(d).

Links

Robert Israel, Table of n, a(n) for n = 0..223

Formula

From Robert Israel, Jun 01 2025: (Start)

a(n) = 4*n^2 * a(n-1) + 4^n*n!.

a(n) = 4^n * e * Gamma(n+1, 1) * n!.

(End)

Maple

g:= proc(n) option remember;
  4*n^2 * procname(n-1) + 4^n*n!
end proc:
g(0):= 1:
map(g, [$0..30]); # Robert Israel, Jun 01 2025

Crossrefs

Sequence in context: A036909 A369539 A221077 * A219265 A300466 A184605

Adjacent sequences: A052137 A052138 A052139 * A052141 A052142 A052143

Keyword

nonn

Author

N. J. A. Sloane, Jan 23 2000

Status

approved