login
A190734
Central coefficients of the Riordan matrix A121576.
0
1, 5, 51, 618, 8043, 108753, 1505652, 21181632, 301445115, 4327546335, 62550664827, 909065484726, 13271032349844, 194464001709708, 2858582670411768, 42135099729748512, 622533141544186779, 9216768941364987195, 136706015987753749593
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
Cf. A121576.
Sequence in context: A370172 A180511 A245926 * A154886 A356586 A268138
KEYWORD
nonn
AUTHOR
Emanuele Munarini, May 18 2011
STATUS
approved