A183145 G.f.: Sum_{n>=0} [Sum_{k=0..n} C(n,k)^3*x^k]^2 * x^n.
1, 1, 3, 18, 121, 928, 6240, 46617, 360997, 2889223, 23635458, 195429765, 1643489944, 13988813548, 120403750665, 1045933596357, 9158182856203, 80773120032142, 716955897008481, 6400569497637804, 57436282624514236
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 121*x^4 + 928*x^5 + 6240*x^6 +... which equals the sum of the series: A(x) = 1 + (1 + x)^2*x + (1 + 2^3*x + x^2)^2*x^2 + (1 + 3^3*x + 3^3*x^2 + x^3)^2*x^3 + (1 + 4^3*x + 6^3*x^2 + 4^3*x^3 + x^4)^2*x^4 + (1 + 5^3*x + 10^3*x^2 + 10^3*x^3 + 5^3*x^4 + x^5)^2*x^5 + (1 + 6^3*x + 15^3*x^2 + 20^3*x^3 + 15^3*x^4 + 6^3*x^5 + x^6)^2*x^6 +...
Crossrefs
Cf. A183146.
Programs
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PARI
{a(n)=polcoeff(sum(m=0,n,sum(k=0,m,binomial(m,k)^3*x^k)^2*x^m)+x*O(x^n),n)}