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

0,2

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = 2^n*(2^n + 1)^(n-1) for n>0 with a(0)=1.

Example

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 +...

Prog

(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))}

Crossrefs

Cf. A171801, A171800, A136516.

Sequence in context: A168480 A364886 A198761 * A251183 A158268 A168407

Adjacent sequences: A171796 A171797 A171798 * A171800 A171801 A171802

Keyword

nonn

Author

Paul D. Hanna, Jan 20 2010

Status

approved