A377642 - OEIS

%I #42 Nov 16 2024 14:57:54

%S 1,2,12,224,13440,2666496,1791885312,4161269661696,33955960439439360,

%T 987107315743488737280,103404624282172311371513856,

%U 39408968779516596852827017445376,55084280201257118417007491904448757760,284322478318511376197290687371005495020093440

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

%H Nikita Babich, <a href="/A377642/b377642.txt">Table of n, a(n) for n = 1..100</a>

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

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

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

%F a(n) ~ A048651 * 2^(n*(n-1)) / (n-1)!. - _Vaclav Kotesovec_, Nov 13 2024

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

%o (PARI) a(n)=prod(i=1, n-1, 2^n-2^i)/(n-1)! \\ _Andrew Howroyd_, Nov 10 2024

%Y Appears to be main diagonal of A270882.

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

%K nonn,easy

%O 1,2

%A _Nikita Babich_, Nov 05 2024