A193198 G.f.: A(x) = Sum_{n>=0} x^n/(1 - 3^n*x)^n.

1, 1, 4, 28, 352, 7696, 296704, 19845568, 2325071872, 472050401536, 167325747134464, 102717666720160768, 109887628080679616512, 203517277347030338768896, 656102983404750860283019264, 3660938644168893995628877692928

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..90

Formula

a(n) = Sum_{k=0..n-1} binomial(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, A135079, 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