OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Emanuele Munarini, May 18 2011
STATUS
approved