A116881 Row sums of triangle A116880 (generalized Catalan C(1,2)).

1, 4, 23, 150, 1037, 7408, 54035, 399850, 2990105, 22540260, 170991647, 1303789534, 9983164453, 76711854040, 591236890667, 4568611684306, 35382196437041, 274564234870732, 2134337640202295, 16617270658727878

Offset

0,2

Links

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

Formula

a(n) = Sum_{m=0,..,n} A116880(n,m), n>=0.

G.f.: (32*x^2+12*sqrt(1-8*x)*x-4*x)/(-32*x^3+sqrt(1-8*x)*(8*x^2+7*x-1)-36*x^2-3*x+1). - Vladimir Kruchinin, Nov 23 2014

a(n) = sum(k=0..n, ((k+1)^2*binomial(2*(n+1),n-k)*binomial(n+k+2,n+1))/((n+k+1)*(n+k+2))). - Vladimir Kruchinin, Nov 23 2014

a(n) ~ 2^(3*n+3) / (9*sqrt(Pi*n)). - Vaclav Kotesovec, Nov 23 2014

Conjecture: n*(3*n-4)*a(n) +(-21*n^2+43*n-10)*a(n-1) -4*(3*n-1)*(2*n-1)*a(n-2)=0. - R. J. Mathar, Jun 22 2016

Mathematica

CoefficientList[Series[(32 x^2 + 12 Sqrt[1 - 8 x] x - 4 x) / (-32 x^3 + Sqrt[1 - 8 x] (8 x^2 + 7 x - 1) - 36 x^2 - 3 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 23 2014 *)

Prog

(Maxima) a(n):=sum(((k+1)^2*binomial(2*(n+1), n-k)*binomial(n+k+2, n+1))/((n+k+1)*(n+k+2)), k, 0, n); /* Vladimir Kruchinin, Nov 23 2014 */

Crossrefs

Sequence in context: A357152 A146964 A194006 * A107089 A350480 A193113

Adjacent sequences: A116878 A116879 A116880 * A116882 A116883 A116884

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 24 2006

Status

approved