A130655 Catalan transform of Catalan numbers C(n+1).

1, 2, 7, 28, 119, 524, 2363, 10844, 50446, 237280, 1126437, 5389916, 25967972, 125868952, 613385075, 3003586196, 14771851093, 72936101780, 361419276386, 1796837068400, 8960207761500

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} A106566(n,k)*A000108(k+1).

Conjecture: 3*n*(n-2)*(n+2)*a(n) +4*(-10*n^3+21*n^2+7*n-15)*a(n-1) +16*(11*n^3-47*n^2+57*n-15)*a(n-2) -8*(2*n-5)*(4*n-9)*(4*n-7)*a(n-3)=0. - R. J. Mathar, Mar 01 2015

G.f.: (C(x*C(x))-1)/(x*C(x)), where C(x) is g.f. of Catalan numbers A000108. - Vladimir Kruchinin, Jul 02 2015

a(n) ~ 2^(4*n+3/2) / (sqrt(Pi) * n^(3/2) * 3^(n-1/2)). - Vaclav Kotesovec, Jul 02 2015

Maple

A130655 := proc(n)
    add(A106566(n, k)*A000108(k+1), k=0..n) ;
end proc: # R. J. Mathar, Mar 01 2015

Mathematica

CoefficientList[Series[2/(Sqrt[-1 + 2*Sqrt[1-4*x]] + Sqrt[1-4*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 02 2015 *)

Prog

(PARI) x='x+O('x^50); Vec(2/(sqrt(-1 + 2*sqrt(1-4*x)) + sqrt(1-4*x))) \\ G. C. Greubel, Mar 21 2017

Crossrefs

Cf. A127632, A129442.

Sequence in context: A151298 A161944 A150652 * A150653 A150654 A150655

Adjacent sequences: A130652 A130653 A130654 * A130656 A130657 A130658

Keyword

nonn

Author

Philippe Deléham, Jun 21 2007

Status

approved