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A193199 G.f.: A(x) = Sum_{n>=0} x^n/(1 - 4^n*x)^n. 1
1, 1, 5, 49, 1025, 42241, 3610625, 609251329, 210923290625, 144320565411841, 201501092228890625, 556475188311619534849, 3125896980250691972890625, 34751531654955460673195212801, 784223845648499469575195012890625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = Sum_{k=0..n-1} C(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: A001819 A064618 A249588 * A224680 A075986 A251657

Adjacent sequences:  A193196 A193197 A193198 * A193200 A193201 A193202

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 17 2011

STATUS

approved

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Last modified October 27 06:10 EDT 2021. Contains 348271 sequences. (Running on oeis4.)