A183146 G.f.: Sum_{n>=0} [Sum_{k=0..n} C(n,k)^2*x^k]^3 * x^n.

1, 1, 4, 16, 80, 407, 2221, 12380, 71196, 417016, 2484839, 15001779, 91603298, 564661194, 3509278042, 21964437947, 138330334357, 875977578584, 5574225259696, 35626247068500, 228592067446715, 1471959684881231

Offset: 0

Author

Paul D. Hanna, Dec 26 2010

Keywords

• nonn

Comments

Compare g.f. to a g.f. of the Whitney numbers in A051286:

Sum_{n>=0} [Sum_{k=0..n} C(n,k)^2*x^k] * x^n.

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 16*x^3 + 80*x^4 + 407*x^5 + 2221*x^6 +...
which equals the sum of the series:
A(x) = 1 + (1 + x)^3*x + (1 + 4*x + x^2)^3*x^2
+ (1 + 9*x + 9*x^2 + x^3)^3*x^3
+ (1 + 16*x + 36*x^2 + 16*x^3 + x^4)^3*x^4
+ (1 + 25*x + 100*x^2 + 100*x^3 + 25*x^4 + x^5)^3*x^5
+ (1 + 36*x + 225*x^2 + 400*x^3 + 225*x^4 + 36*x^5 + x^6)^3*x^6 +...
		

Crossrefs

Cf. A180717, A051286.

Programs

PARI

{a(n)=polcoeff(sum(m=0,n,sum(k=0,m,binomial(m,k)^2*x^k)^3*x^m)+x*O(x^n),n)}