%I #11 Sep 08 2022 08:46:21
%S 1,2,6,28,210,2604,54684,1984248,126495810,14364301980,2938936185108,
%T 1093818612893832,746531203300040340,940744167112404680760,
%U 2201744527114646554984440,9619275055995416488956686064,78799898849332452450472052650530
%N a(n) = (2^n / n!) * (2^1 - 1) * (2^2 - 1) * ... * (2^n - 1).
%C a(n) = b[n, 0, 1] in A157285.
%H G. C. Greubel, <a href="/A305627/b305627.txt">Table of n, a(n) for n = 0..85</a>
%F 0 = +a(n)*(+a(n+1)*(+2*a(n+3)) +a(n+2)*(-6*a(n+2) +a(n+3))) +a(n+1)*(+a(n+1)*(+4*a(n+2) - 4*a(n+3)) +a(n+2)*(+4*a(n+2))) for all n in Z.
%t a[ n_] := If[n < 0, 0, QPochhammer[2, 2, n] (-2)^n / n!];
%o (PARI) {a(n) = if( n<0, 0, prod(k=1, n, 2^k - 1) * 2^n / n!)};
%o (Magma) [1] cat [(&*[(2*k-1): k in [1..n]])*2^n/Factorial(n): n in [1..20]]; // _G. C. Greubel_, Jul 28 2018
%Y Cf. A157285.
%K nonn,easy
%O 0,2
%A _Michael Somos_, Jun 06 2018