A166896 G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k] * x^n/n ), an integer series in x.

1, 1, 2, 6, 16, 45, 142, 459, 1508, 5122, 17787, 62649, 223971, 811339, 2970032, 10974150, 40893393, 153512844, 580082454, 2205046961, 8427087958, 32362949488, 124837337235, 483508287359, 1879669861074, 7332469937755

Offset: 0

Author

Paul D. Hanna, Nov 23 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 16*x^4 + 45*x^5 + 142*x^6 + 459*x^7 +...
log(A(x)) = x + 3*x^2/2 + 13*x^3/3 + 39*x^4/4 + 126*x^5/5 + 477*x^6/6 + 1765*x^7/7 +...+ A166897(n)*x^n/n +...
		

Crossrefs

Cf. A166897, variants: A166894, A166898.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^3*x^k)*x^m/m)+x*O(x^n)), n)}

PARI

{a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m\2, binomial(m-k, k)^3*m/(m-k))*x^m/m)+x*O(x^n)), n)}

Formula

G.f.: exp( Sum_{n>=1} A166897(n)*x^n/n ) where A166897(n) = Sum_{k=0..[n/2]} C(n-k,k)^3*n/(n-k).