A193190 G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1 - 4^(n-k)*x^k).

1, 1, 2, 6, 35, 394, 8804, 397482, 35759656, 6485002635, 2338622693988, 1698239604693650, 2450945990748440102, 7121092086085582889354, 41114705331946969977079884, 477857552284771772990908082576

Offset

0,3

Links

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

Formula

G.f. satisfies: A(4*x) = Sum_{n>=0} 4^n*x^n/Product_{k=1..n} (1-4^n*x^k).

Example

 G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 35*x^4 + 394*x^5 + 8804*x^6 +...
where:
A(x) = 1 + x/(1-x) + x^2/((1-4*x)*(1-x^2)) + x^3/((1-16*x)*(1-4*x^2)*(1-x^3)) + x^4/((1-64*x)*(1-16*x^2)*(1-4*x^3)*(1-x^4)) +...

Prog

 (PARI) {a(n)=local(A=1); polcoeff(sum(m=0, n, x^m/prod(k=1, m, 1-4^(m-k)*x^k +x*O(x^n))), n)}

Crossrefs

Cf. A193188, A193189, A193191.

Sequence in context: A107868 A334162 A173399 * A247209 A324577 A324582

Adjacent sequences: A193187 A193188 A193189 * A193191 A193192 A193193

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2011

Status

approved