A183145 - OEIS

%I #8 Mar 12 2022 13:25:18

%S 1,1,3,18,121,928,6240,46617,360997,2889223,23635458,195429765,

%T 1643489944,13988813548,120403750665,1045933596357,9158182856203,

%U 80773120032142,716955897008481,6400569497637804,57436282624514236

%N G.f.: Sum_{n>=0} [Sum_{k=0..n} C(n,k)^3*x^k]^2 * x^n.

%e G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 121*x^4 + 928*x^5 + 6240*x^6 +...

%e which equals the sum of the series:

%e A(x) = 1 + (1 + x)^2*x + (1 + 2^3*x + x^2)^2*x^2

%e + (1 + 3^3*x + 3^3*x^2 + x^3)^2*x^3

%e + (1 + 4^3*x + 6^3*x^2 + 4^3*x^3 + x^4)^2*x^4

%e + (1 + 5^3*x + 10^3*x^2 + 10^3*x^3 + 5^3*x^4 + x^5)^2*x^5

%e + (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 +...

%o (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)}

%Y Cf. A183146.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 26 2010