A377642 a(n) = (1/(n-1)!) * Product_{i=1..n-1} (2^n-2^i).

1, 2, 12, 224, 13440, 2666496, 1791885312, 4161269661696, 33955960439439360, 987107315743488737280, 103404624282172311371513856, 39408968779516596852827017445376, 55084280201257118417007491904448757760, 284322478318511376197290687371005495020093440

Offset: 1

Author

Nikita Babich, Nov 05 2024

Keywords

• nonn
• easy

Links

• Nikita Babich, Table of n, a(n) for n = 1..100

Crossrefs

Appears to be main diagonal of A270882.

Cf. A000079, A000142, A002884, A028365, A048651, A053601.

Programs

Mathematica

Table[Product[2^n - 2^i, {i, 1, n - 1}]/Factorial[n - 1], {n, 1, 20}]

PARI

a(n)=prod(i=1, n-1, 2^n-2^i)/(n-1)! \\ Andrew Howroyd, Nov 10 2024

Formula

a(n) = (Product_{i=1..n-1}(2^n-2^i))/((n-1)!).

a(n) = A028365(n-1)/A000142(n-1).

a(n) = A000079(n-1) * A053601(n-1).

a(n) ~ A048651 * 2^(n*(n-1)) / (n-1)!. - Vaclav Kotesovec, Nov 13 2024