A374021 Row products of A351153.

1, 1, 3, 24, 400, 11700, 536256, 35631232, 3245577984, 388702800000, 59265098200000, 11212953038217216, 2578459154484215808, 708372581870426497024, 229171184991141120000000, 86242576440372042240000000, 37355382389967084527220883456, 18452600861204793901808906698752

Offset: 0

Author

Stefano Spezia, Jun 25 2024

Keywords

• nonn

Crossrefs

Cf. A005408, A033996, A351153.

Programs

Mathematica

A351153[n_,k_]:=n(k-1)-k(k-3)/2; a[n_]:=Product[A351153[n,k],{k,n}]; Array[a,18,0]

PARI

a(n) = vecprod(vector(n, k, n*(k - 1) - k*(k - 3)/2)); \\ Michel Marcus, Jun 25 2024

Formula

a(n) = (-1/2)^n*Pochhammer((b(n)-2*n-1)/2, n)*Pochhammer((-b(n)-2*n-1)/2, n), where b(n) = sqrt(A033996(n) + 9).

a(n) ~ sqrt(Pi) * 2^(n+2) * n^(2*n - 3/2) / exp(2*n). - Vaclav Kotesovec, Jun 27 2024