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

0,2

Links

Table of n, a(n) for n=0..10.

Formula

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

Example

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 +...

Prog

(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))}

Crossrefs

Cf. A171799, A171800.

Sequence in context: A013113 A009105 A168481 * A091797 A265230 A007726

Adjacent sequences: A171798 A171799 A171800 * A171802 A171803 A171804

Keyword

nonn

Author

Paul D. Hanna, Jan 20 2010

Status

approved