A386863 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(3*n+1,k) * binomial(3*n-k-1,n-k).
1, 8, 117, 1948, 34283, 622272, 11519692, 216193460, 4098365799, 78293227384, 1504814127893, 29066030323920, 563717999500852, 10970568626688704, 214125123753359544, 4189892211091193380, 82166338354628744159, 1614453403457943056184, 31776198133079795063887
Offset: 0
Keywords
Programs
-
PARI
a(n) = sum(k=0, n, 2^(n-k)*binomial(3*n+1, k)*binomial(3*n-k-1, n-k));
Formula
a(n) = [x^n] (1+x)^(3*n+1)/(1-2*x)^(2*n).
a(n) = [x^n] 1/((1-x)^2 * (1-3*x)^(2*n)).
a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * (n-k+1) * binomial(3*n+1,k).
a(n) = Sum_{k=0..n} 3^k * (n-k+1) * binomial(2*n+k-1,k).