A323540 a(n) = Product_{k=0..n} (k^2 + (n-k)^2).

0, 1, 32, 2025, 204800, 30525625, 6307891200, 1727713080625, 606076928000000, 265058191985900625, 141409376995328000000, 90403125002859606705625, 68229510086445571768320000, 60026603304487418050791015625, 60893916244529680380723200000000

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..221

Crossrefs

Cf. A272244, A323425, A323541, A323542, A323543, A323544, A323545, A323546.

Cf. 2*A000330 and A006331 (with sum instead of product).

Programs

Magma

m:=2; [(&*[k^m + (n-k)^m: k in [0..n]]): n in [0..20]]; // G. C. Greubel, Jan 18 2019

Mathematica

Table[Product[k^2+(n-k)^2, {k, 0, n}], {n, 0, 20}]

PARI

m=2; vector(20, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ G. C. Greubel, Jan 18 2019

Sage

m=2; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..20)] # G. C. Greubel, Jan 18 2019

Formula

a(n) ~ exp((Pi-4)*n/2) * n^(2*n+2).