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

0,2

Links

Table of n, a(n) for n=0..18.

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

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

Prog

(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);

Crossrefs

Cf. A121576.

Sequence in context: A370172 A180511 A245926 * A154886 A356586 A268138

Adjacent sequences: A190731 A190732 A190733 * A190735 A190736 A190737

Keyword

nonn

Author

Emanuele Munarini, May 18 2011

Status

approved