A386836 a(n) = Sum_{k=0..n} binomial(3*n+2,k) * binomial(3*n-k-1,n-k).
1, 7, 70, 782, 9199, 111465, 1376764, 17234600, 217891693, 2775766091, 35574777154, 458169648722, 5924747347835, 76876586813629, 1000418599504408, 13051488907037580, 170643358430006553, 2235400439909584575, 29333436132847784062, 385507257723471794774, 5073372058467119928391
Offset: 0
Keywords
Programs
-
PARI
a(n) = sum(k=0, n, binomial(3*n+2, k)*binomial(3*n-k-1, n-k));
Formula
a(n) = [x^n] (1+x)^(3*n+2)/(1-x)^(2*n).
a(n) = [x^n] 1/((1-x)^3 * (1-2*x)^(2*n)).
a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(3*n+2,k) * binomial(n-k+2,n-k).
a(n) = Sum_{k=0..n} 2^k * binomial(2*n+k-1,k) * binomial(n-k+2,n-k).