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A193198 G.f.: A(x) = Sum_{n>=0} x^n/(1 - 3^n*x)^n. 1
1, 1, 4, 28, 352, 7696, 296704, 19845568, 2325071872, 472050401536, 167325747134464, 102717666720160768, 109887628080679616512, 203517277347030338768896, 656102983404750860283019264, 3660938644168893995628877692928 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(n) = Sum_{k=0..n-1} C(n-1,k)*3^(k*(n-k)) for n>0 with a(0)=1.

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 28*x^3 + 352*x^4 + 7696*x^5 +...

where:

A(x) = 1 + x/(1-3*x) + x^2/(1-9*x)^2 + x^3/(1-27*x)^3 + x^4/(1-81*x)^4 +...

PROG

(PARI) {a(n)=local(A=1); A=1+sum(m=1, n, x^m/(1-3^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)*3^(k*(n-k))))}

CROSSREFS

Cf. A000684, A193199.

Sequence in context: A080636 A223887 A140425 * A165193 A309147 A217903

Adjacent sequences:  A193195 A193196 A193197 * A193199 A193200 A193201

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 17 2011

STATUS

approved

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Last modified September 20 12:05 EDT 2021. Contains 347586 sequences. (Running on oeis4.)