A206139 G.f.: A(x) = Sum_{n>=0} x^(n*(n+1)/2) / Product_{k=1..n} (1-x^k)^(n-k+1).

1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 88, 141, 224, 356, 563, 890, 1401, 2202, 3448, 5386, 8386, 13025, 20175, 31180, 48077, 73976, 113588, 174057, 266174, 406224, 618729, 940552, 1427038, 2161122, 3266956, 4930052, 7427314, 11171332, 16776169, 25154204

Offset: 0

Author

Paul D. Hanna, Feb 04 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 13*x^7 +...
where
A(x) = 1 + x/(1-x) + x^3/((1-x)^2*(1-x^2)) + x^6/((1-x)^3*(1-x^2)^2*(1-x^3)) + x^10/((1-x)^4*(1-x^2)^3*(1-x^3)^2*(1-x^4)) +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A206119.

Programs

PARI

{a(n)=polcoeff(sum(m=0,n,x^(m*(m+1)/2)/prod(k=1,m,(1-x^k +x*O(x^n))^(m-k+1))),n)}
for(n=0,61,print1(a(n),", "))