A171801 O.g.f.: Sum_{n>=0} (n+1)*2^(n^2)*x^n/(1 - 2^n*x)^n.

1, 4, 56, 2448, 379168, 223096896, 514098000000, 4691436926959872, 170097530401558168064, 24520599890836361905701888, 14055963692387060312500000000000

Offset: 0

Author

Paul D. Hanna, Jan 20 2010

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 4*x + 56*x^2 + 2448*x^3 + 379168*x^4 +...
A(x) = 1 + 2*2*x/(1-2*x) + 3*2^4*x^2/(1-2^2*x)^2 + 4*2^9*x^3/(1-2^3*x)^3 +...
		

Crossrefs

Cf. A171799, A171800.

Programs

PARI

{a(n)=polcoeff(sum(m=0,n,(m+1)*2^(m^2)*x^m/(1-2^m*x+x*O(x^n))^m),n)}

PARI

{a(n)=if(n==0,1,2^n*((n+1)*2^n + 2)*(2^n + 1)^(n-2))}

Formula

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