A386833 a(n) = Sum_{k=0..n} binomial(3*n+1,k) * binomial(3*n-k-1,n-k).
1, 6, 59, 656, 7701, 93210, 1150495, 14395428, 181936169, 2317140014, 29691138099, 382334271544, 4943464235069, 64137141682242, 834561532624967, 10886878474010700, 142332442919829585, 1864423992564121686, 24464149489904517211, 321499324010641490016, 4230840338116037836901
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(3*n-k-1, n-k));
Formula
a(n) = [x^n] (1+x)^(3*n+1)/(1-x)^(2*n).
a(n) = [x^n] 1/((1-x)^2 * (1-2*x)^(2*n)).
a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * (n-k+1) * binomial(3*n+1,k).
a(n) = Sum_{k=0..n} 2^k * (n-k+1) * binomial(2*n+k-1,k).