A301616 a(n) = Product_{k=1..n} (k^2+(n-k+1)^2).

1, 2, 25, 800, 48841, 4867200, 719580625, 147968000000, 40399053800625, 14140937699532800, 6174655078400355625, 3290389182409605120000, 2101698235513021884765625, 1585118602783467315200000000, 1393789829051727854522489390625

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..200

Formula

a(n) = A302661(n)^2 + A302662(n)^2.

a(n) ~ n^(2*n) / exp(2*n - Pi*(n + 1)/2). - Vaclav Kotesovec, Apr 11 2018

Maple

seq(mul(k^2+(n-k+1)^2, k=1..n), n=0..15); # Muniru A Asiru, Apr 11 2018

Mathematica

Table[Product[k^2 + (n - k + 1)^2, {k, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, Apr 11 2018 *)

Prog

(PARI) {a(n) = prod(k=1, n, k^2+(n-k+1)^2)}
(GAP) List([0..15], n->Product([1..n], k->k^2+(n-k+1)^2)); # Muniru A Asiru, Apr 11 2018

Crossrefs

Cf. A302661, A302662.

Sequence in context: A119829 A059363 A216661 * A298157 A342298 A273545

Adjacent sequences: A301613 A301614 A301615 * A301617 A301618 A301619

Keyword

nonn

Author

Seiichi Manyama, Apr 11 2018

Status

approved