A206100 G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1-x^k)^k.

1, 1, 2, 3, 6, 9, 18, 27, 50, 79, 135, 215, 361, 564, 923, 1450, 2305, 3590, 5645, 8693, 13479, 20611, 31560, 47880, 72601, 109195, 164126, 245109, 365282, 541642, 801380, 1180281, 1734332, 2538490, 3706287, 5392883, 7827571, 11325879, 16348515, 23530961

Offset

0,3

Links

Table of n, a(n) for n=0..39.

Formula

G.f.: 1 + x*(1 - G(0))/(1-x) where G(k) = 1 - 1/(1-x^(k+1))^(k+1)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 23 2013

Example

G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 9*x^5 + 18*x^6 + 27*x^7 +...
where
A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-x^2)^2) + x^3/((1-x)*(1-x^2)^2*(1-x^3)^3) + x^4/((1-x)*(1-x^2)^2*(1-x^3)^3*(1-x^4)^4) +...

Prog

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

Crossrefs

Sequence in context: A062865 A351018 A180684 * A178940 A018264 A081741

Adjacent sequences: A206097 A206098 A206099 * A206101 A206102 A206103

Keyword

nonn

Author

Paul D. Hanna, Feb 03 2012

Status

approved