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

%I A374574 #19 Jul 12 2024 19:11:39
%S A374574 1,3,32,870,46224,4037880,522956160,93928267440,22324392518400,
%T A374574 6780385526302080,2561327494111411200,1177652997443424902400,
%U A374574 647478071469567800985600,419450149241406188889984000,316196664211373618844934963200,274410818470142134209609852672000
%N A374574 a(n) = Sum_{j=n..2n} j!.
%H A374574 Alois P. Heinz, <a href="/A374574/b374574.txt">Table of n, a(n) for n = 0..224</a>
%F A374574 a(n) = a(n-1) - (n-1)! + (2*n-1)! + (2*n)! with a(0) = 1.
%F A374574 a(n) = Sum_{j=0..n} (n + j)!.
%F A374574 a(n) = A100822(2n,n).
%F A374574 a(n) = A143122(2n,n).
%p A374574 a:= proc(n) option remember; `if`(n<3, [1, 3, 32][n+1],
%p A374574      ((16*n^3-16*n^2-n+2)*a(n-1)-(n-1)*(16*n^3-20*n^2+6*n-1)
%p A374574       *a(n-2)+2*(2*n-1)*(4*n+1)*(n-1)*(n-2)*a(n-3))/(4*n-3))
%p A374574     end:
%p A374574 seq(a(n), n=0..15);
%p A374574 # second Maple program:
%p A374574 a:= proc(n) option remember; `if`(n=0, 1,
%p A374574       a(n-1) -(n-1)! +(2*n-1)! +(2*n)!)
%p A374574     end:
%p A374574 seq(a(n), n=0..15);
%Y A374574 Row sums of A143084.
%Y A374574 Cf. A000142, A100822, A143122, A296591 (the same for product).
%Y A374574 Diagonal of A054115, A211370.
%K A374574 nonn
%O A374574 0,2
%A A374574 _Alois P. Heinz_, Jul 11 2024