A374574 a(n) = Sum_{j=n..2n} j!.

1, 3, 32, 870, 46224, 4037880, 522956160, 93928267440, 22324392518400, 6780385526302080, 2561327494111411200, 1177652997443424902400, 647478071469567800985600, 419450149241406188889984000, 316196664211373618844934963200, 274410818470142134209609852672000

Offset: 0

Author

Alois P. Heinz, Jul 11 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..224

Crossrefs

Row sums of A143084.

Cf. A000142, A100822, A143122, A296591 (the same for product).

Diagonal of A054115, A211370.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [1, 3, 32][n+1],
     ((16*n^3-16*n^2-n+2)*a(n-1)-(n-1)*(16*n^3-20*n^2+6*n-1)
      *a(n-2)+2*(2*n-1)*(4*n+1)*(n-1)*(n-2)*a(n-3))/(4*n-3))
    end:
seq(a(n), n=0..15);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1,
      a(n-1) -(n-1)! +(2*n-1)! +(2*n)!)
    end:
seq(a(n), n=0..15);

Formula

a(n) = a(n-1) - (n-1)! + (2*n-1)! + (2*n)! with a(0) = 1.

a(n) = Sum_{j=0..n} (n + j)!.

a(n) = A100822(2n,n).

a(n) = A143122(2n,n).