A171799 O.g.f.: Sum_{n>=0} 2^(n^2)*x^n/(1 - 2^n*x)^n.
1, 2, 20, 648, 78608, 37949472, 74258600000, 589859028828288, 18957096840069579008, 2455889836782322072945152, 1278835681226410156250000000000, 2671465293024628033252951422140418048
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + 2*x + 20*x^2 + 648*x^3 + 78608*x^4 +... A(x) = 1 + 2*x/(1-2*x) + 2^4*x^2/(1-2^2*x)^2 + 2^9*x^3/(1-2^3*x)^3 +...
Programs
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PARI
{a(n)=polcoeff(sum(m=0,n,2^(m^2)*x^m/(1-2^m*x+x*O(x^n))^m),n)} -
PARI
{a(n)=if(n==0,1,2^n*(2^n+1)^(n-1))}
Formula
a(n) = 2^n*(2^n + 1)^(n-1) for n>0 with a(0)=1.