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

0,3

Links

Table of n, a(n) for n=0..20.

Example

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 +...

Prog

(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)}

Crossrefs

Cf. A183146.

Sequence in context: A118348 A011792 A295537 * A127188 A355048 A074558

Adjacent sequences: A183142 A183143 A183144 * A183146 A183147 A183148

Keyword

nonn

Author

Paul D. Hanna, Dec 26 2010

Status

approved