A166897 a(n) = Sum_{k=0..[n/2]} C(n-k,k)^3*n/(n-k), n>=1.

1, 3, 13, 39, 126, 477, 1765, 6495, 24709, 95128, 367368, 1431453, 5620343, 22170543, 87858813, 349708431, 1397003136, 5598513261, 22502171771, 90681323364, 366299212873, 1482827487650, 6014529069540, 24439715146941

Offset: 1

Author

Paul D. Hanna, Nov 23 2009

Keywords

• nonn

Examples

			L.g.f.: L(x) = x + 3*x^2/2 + 13*x^3/3 + 39*x^4/4 + 126*x^5/5 + 477*x^6/6 +...
exp(L(x)) = 1 + x + 2*x^2 + 6*x^3 + 16*x^4 + 45*x^5 + 142*x^6 + 459*x^7 +...+ A166896(n)*x^n/n +...
		

Crossrefs

Cf. A166897, variants: A167539, A166895, A166899.

Programs

Mathematica

Table[Sum[Binomial[n-k,k]^3 n/(n-k),{k,0,Floor[n/2]}],{n,30}] (* Harvey P. Dale, Mar 05 2013 *)

PARI

a(n)=sum(k=0,n\2,binomial(n-k,k)^3*n/(n-k))

Formula

Logarithmic derivative of A166896.

a(n) ~ sqrt(15) * phi^(3*n + 2) / (6*Pi*n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Nov 27 2017