A193199 G.f.: A(x) = Sum_{n>=0} x^n/(1 - 4^n*x)^n.

1, 1, 5, 49, 1025, 42241, 3610625, 609251329, 210923290625, 144320565411841, 201501092228890625, 556475188311619534849, 3125896980250691972890625, 34751531654955460673195212801, 784223845648499469575195012890625

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..80

Formula

a(n) = Sum_{k=0..n-1} binomial(n-1,k)*4^(k*(n-k)) for n>0 with a(0)=1.

Example

G.f.: A(x) = 1 + x + 5*x^2 + 49*x^3 + 1025*x^4 + 42241*x^5 +...
where:
A(x) = 1 + x/(1-4*x) + x^2/(1-16*x)^2 + x^3/(1-64*x)^3 + x^4/(1-256*x)^4 +...

Prog

(PARI) {a(n)=local(A=1); A=1+sum(m=1, n, x^m/(1-4^m*x +x*O(x^n))^m); polcoeff(A, n)}
(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, binomial(n-1, k)*4^(k*(n-k))))}

Crossrefs

Cf. A000684, A193198.

Sequence in context: A249588 A348901 A363480 * A224680 A075986 A251657

Adjacent sequences: A193196 A193197 A193198 * A193200 A193201 A193202

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2011

Status

approved