A191585 Central coefficients of the Riordan matrix (1/(1-3*x^2),x/(1-x)) (A191582).

1, 1, 6, 19, 74, 276, 1056, 4047, 15606, 60382, 234356, 911802, 3554864, 13883650, 54304788, 212687199, 833958918, 3273341382, 12859792932, 50562992490, 198954466524, 783371113152, 3086377703184, 12166795814166, 47987669811276, 189361785529476

Offset: 0

Author

Emanuele Munarini, Jun 07 2011

Keywords

• nonn

Crossrefs

Cf. A191582.

Programs

Mathematica

Table[Sum[Binomial[2n-2i-1,n-2i]3^i,{i,0,n/2}],{n,0,25}]
CoefficientList[Series[(2-11x+12x^2+(2-9x)Sqrt[1-4x])/(2(1-4x)(2- 6x-9x^2)),{x,0,30}],x] (* Harvey P. Dale, Jun 10 2011 *)

Maxima

makelist(sum(binomial(2*n-2*i-1,n-2*i)*3^i,i,0,n/2),n,0,25);

Formula

a(n) = T(2*n,n), where T(n,k) = A...(n,k).

a(n) = sum(binomial(2*n-2*i-1,n-2*i)*3^i,i=0..n/2).

G.f.: (2-11*x+12*x^2+(2-9*x)*sqrt(1-4*x))/(2*(1-4*x)*(2-6*x-9*x^2)).

Conjecture: 2*n*(n+3)*a(n) +2*(-7*n^2-19*n+24)*a(n-1) +3*(5*n^2+11*n-48)*a(n-2) +18*(n+4)*(2*n-3)*a(n-3)=0. - R. J. Mathar, Jun 14 2016

Conjecture: +4*n*a(n) +2*(-23*n+22)*a(n-1) +156*(n-2)*a(n-2) +9*(-7*n+38)*a(n-3) +162*(-2*n+5)*a(n-4)=0. - R. J. Mathar, Jun 14 2016