A323545 a(n) = Product_{k=0..n} (k^7 + (n-k)^7).

0, 1, 32768, 79593387129, 328983774635229184, 8781626117710113525390625, 570409595340477623191338982834176, 112244673425189306235795780017831813874289, 49449149324106963036650868175987491957290049732608, 48527312221741371319651099141827554314119977393170380398241

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..79

Crossrefs

Cf. A323535, A323540, A323541, A323542, A323543, A323544, A323546, A320345.

Cf. 2*A000541 (with sum instead of product).

Programs

Magma

m:=7; [(&*[k^m + (n-k)^m: k in [0..n]]): n in [0..10]]; // G. C. Greubel, Jan 18 2019

Mathematica

Table[Product[k^7+(n-k)^7, {k, 0, n}], {n, 0, 10}]

PARI

m=7; vector(10, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ G. C. Greubel, Jan 18 2019

Sage

m=7; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..10)] # G. C. Greubel, Jan 18 2019

Formula

a(n) ~ exp((8*cos((Pi + arctan(2769*sqrt(3)/239))/6)*Pi/sqrt(21)-6)*n) * n^(7*n+7).

Equivalently, a(n) ~ exp((4*Pi*sqrt(2*(13 + 19*sin(Pi/14) - sin(3*Pi/14))/7)/7 - 6)*n) * n^(7*n+7). - Vaclav Kotesovec, Jan 23 2019