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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 17 2011
STATUS
approved