A375839 a(n) = Product_{k=0..n} (k^2 + n).

0, 2, 36, 1008, 41600, 2381400, 180457200, 17467670528, 2100621828096, 306960977700000, 53529274174376000, 10973787848179200000, 2611472797582941487104, 713649909809783275801472, 221870902844468552220000000, 77837994361783539267010560000

Offset: 0

Author

Vaclav Kotesovec, Aug 31 2024

Keywords

• nonn

Crossrefs

Cf. A156648, A101686.

Cf. A375840, A375841, A375842, A375843, A375844, A375845.

Programs

Mathematica

Table[Product[k^2 + n, {k, 0, n}], {n, 0, 15}]
Round[Table[Sqrt[n] * Gamma[1 - I*Sqrt[n] + n] * Gamma[1 + I*Sqrt[n] + n] * Sinh[Sqrt[n]*Pi] / Pi, {n, 0, 15}]]

Formula

a(n) ~ n^(2*n + 3/2) / exp(2*n - Pi*n^(1/2) + 1).