A190734 Central coefficients of the Riordan matrix A121576.

1, 5, 51, 618, 8043, 108753, 1505652, 21181632, 301445115, 4327546335, 62550664827, 909065484726, 13271032349844, 194464001709708, 2858582670411768, 42135099729748512, 622533141544186779, 9216768941364987195, 136706015987753749593

Offset: 0

Author

Emanuele Munarini, May 18 2011

Keywords

• nonn

Crossrefs

Cf. A121576.

Programs

Mathematica

Sum[Binomial[2n,i]Binomial[3n-i,2n](4-9i+3i^2-12(i-1)n+8n^2)/((2n-i+2)(2n-i+1))2^i,{i,0,n}]/2

Maxima

makelist(sum(binomial(2*n,i)*binomial(3*n-i,2*n)*(4-9*i+3*i^2-12*(i-1)*n+8*n^2)/((2*n-i+2)*(2*n-i+1))*2^i,i,0,n)/2,n,0,12);

Formula

a(n) = [x^n](1-2*x-2*x^2)*(1+2*x)^(2*n)/(1-x)^(2*n+1).

a(n) = sum(i=0..n, binomial(2*n,i) * binomial(3*n-i,2*n) * (8*n^2-12*(i-1)*n+3*i^2-9*i+4) / ((2*n-i+2)*(2*n-i+1))*2^i)/2