A293290 a(n) = Product_{1 <= j <= k <= n} (k^2 + j^2).

1, 2, 80, 187200, 50918400000, 2675955409920000000, 40702283662588674048000000000, 250658664786823821917343252480000000000000, 832906513114759565863066815448211678822400000000000000000, 1919381816160714520414106848157314737202346840876384256000000000000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Formula

a(n) ~ sqrt(Gamma(1/4)) * Pi^(-1/8) * 2^(n^2/2 + n - 1/8) * exp(Pi*n*(n+1)/4 - 3*n^2/2 - n + Pi/24) * n^(n*(n+1) + 1/4). - Vaclav Kotesovec, Feb 26 2019

Mathematica

Table[Product[k^2 + j^2, {k, 1, n}, {j, 1, k}], {n, 0, 10}]

Prog

(Sage) [prod([prod([k^2+j^2 for j in range(1, k+1)]) for k in range(1, n+1)]) for n in range(10)] # Danny Rorabaugh, Oct 16 2017

Crossrefs

Suggested by Omar E. Pol from A264596 formula.

Cf. A101686, A203475, A324403.

Sequence in context: A156932 A291331 A369468 * A056972 A051391 A041799

Adjacent sequences: A293287 A293288 A293289 * A293291 A293292 A293293

Keyword

easy,nonn

Author

Velin Yanev, Oct 05 2017

Status

approved