A368806 a(n) = Product_{i=1..j, j=1..k, k=1..n} i*j*k.

1, 1, 64, 60466176, 504857282956046106624, 46005119909369701466112000000000000000000000, 101230154592156481700985865260692304243040378536591360000000000000000000000000000

Offset: 0

Author

Vaclav Kotesovec, Jan 06 2024

Keywords

• nonn

Crossrefs

Cf. A091868, A255269, A306594, A324427.

Programs

Mathematica

Table[Product[Product[Product[i*j*k, {i,1,j}], {j,1,k}], {k,1,n}], {n, 0, 6}]
Table[Product[k^(k*(k+1)/2) * k!^(k+1), {k, 1, n}], {n, 0, 6}]

Formula

a(n) = Product_{k=1..n} k^(k*(k+1)/2) * k!^(k+1).

a(n) ~ (2*Pi)^(n^2/4 + 3*n/4 + 1/2) * n^(n^3/2 + 7*n^2/4 + 7*n/4 + 1/2) / exp(n^3/2 + 3*n^2/2 + 23*n/24 - 1/8).