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A116881 Row sums of triangle A116880 (generalized Catalan C(1,2)). 2
1, 4, 23, 150, 1037, 7408, 54035, 399850, 2990105, 22540260, 170991647, 1303789534, 9983164453, 76711854040, 591236890667, 4568611684306, 35382196437041, 274564234870732, 2134337640202295, 16617270658727878 (list; graph; refs; listen; history; text; internal format)
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: A020079 A146964 A194006 * A107089 A193113 A192730

Adjacent sequences:  A116878 A116879 A116880 * A116882 A116883 A116884

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Mar 24 2006

STATUS

approved

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Last modified February 28 14:16 EST 2021. Contains 341707 sequences. (Running on oeis4.)