A193189 G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1 - 3^(n-k)*x^k).

1, 1, 2, 5, 21, 143, 1669, 33857, 1193884, 73213398, 7782525256, 1435756825940, 458580933408939, 254032043880526955, 243538638598143498007, 404846375019050008264450, 1164567481729705354758216971, 5808325975811136555473345566847

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 21*x^4 + 143*x^5 + 1669*x^6 +...
where:
A(x) = 1 + x/(1-x) + x^2/((1-3*x)*(1-x^2)) + x^3/((1-9*x)*(1-3*x^2)*(1-x^3)) + x^4/((1-27*x)*(1-9*x^2)*(1-3*x^3)*(1-x^4)) + ...

Prog

(PARI) {a(n)=local(A=1); polcoeff(sum(m=0, n, x^m/prod(k=1, m, 1-3^(m-k)*x^k +x*O(x^n))), n)}

Crossrefs

Cf. A193188, A193190, A193191.

Sequence in context: A139153 A180998 A144271 * A358316 A176527 A117261

Adjacent sequences: A193186 A193187 A193188 * A193190 A193191 A193192

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2011

Status

approved