A193188 G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1 - 2^(n-k)*x^k).

1, 1, 2, 4, 11, 38, 180, 1182, 10990, 145271, 2729980, 72836122, 2755533950, 147695390782, 11209247627416, 1204126434867322, 183035972377206269, 39363771818346412010, 11975532663667690562398, 5153451004764204946993962

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

G.f. satisfies: A(2*x) = Sum_{n>=0} 2^n*x^n/Product_{k=1..n} (1-2^n*x^k).

Example

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 11*x^4 + 38*x^5 + 180*x^6 +...
where:
A(x) = 1 + x/(1-x) + x^2/((1-2*x)*(1-x^2)) + x^3/((1-4*x)*(1-2*x^2)*(1-x^3)) + x^4/((1-8*x)*(1-4*x^2)*(1-2*x^3)*(1-x^4)) + ...

Prog

(PARI) {a(n)=local(A=1); polcoeff(sum(m=0, n, x^m/prod(k=1, m, 1-2^(m-k)*x^k +x*O(x^n))), n)}

Crossrefs

Cf. A193189, A193190, A193191.

Sequence in context: A107107 A243565 A101898 * A216810 A065851 A173938

Adjacent sequences: A193185 A193186 A193187 * A193189 A193190 A193191

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2011

Status

approved