A161798 G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^3)^2.

1, 2, 9, 46, 262, 1590, 10081, 65986, 442518, 3024772, 20996141, 147603198, 1048747751, 7519252606, 54332565330, 395264527626, 2892666314150, 21281120904168, 157299607827727, 1167582500757800, 8699515577902203

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Vaclav Kotesovec, Recurrence

Formula

a(n) = Sum_{k=0..n} C(2*n-k+1,k)/(n-k+1) * C(n+2*k-1,n-k).

Let A(x)^m = Sum_{n>=0} a(n,m)*x^n then

a(n,m) = Sum_{k=0..n} C(2*n-k+m,k)*m/(n-k+m) * C(n+2*k-1,n-k).

a(n) ~ c*d^n/(sqrt(Pi)*n^(3/2)), where d = 8.01957328653868383... is the root of the equation 3125 + 22356*d - 162432*d^2 - 361584*d^3 - 326592*d^4 + 46656*d^5 = 0 and c = 1.216730444416766043545857948227854793382399566... - Vaclav Kotesovec, Sep 18 2013

Mathematica

Table[Sum[Binomial[2*n-k+1, k]/(n-k+1)*Binomial[n+2*k-1, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 18 2013 *)

Prog

(PARI) {a(n, m=1)=sum(k=0, n, binomial(2*n-k+m, k)*m/(n-k+m)*binomial(n+2*k-1, n-k))}

Crossrefs

Cf. A161797, A161799.

Sequence in context: A020053 A114194 A218045 * A365855 A134091 A219614

Adjacent sequences: A161795 A161796 A161797 * A161799 A161800 A161801

Keyword

nonn

Author

Paul D. Hanna, Jun 19 2009

Status

approved