A383326 a(n) = Sum_{k=0..n} binomial(3*n+1,k) * binomial(3*n-k,n-k).
1, 7, 71, 799, 9439, 114687, 1419263, 17791487, 225172991, 2870945791, 36819740671, 474470776831, 6138443497471, 79681448443903, 1037278449106943, 13536444411412479, 177030837540093951, 2319618918724403199, 30444928900076666879, 400189735705069486079, 5267487129636270243839
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(3*n-k, n-k));
Formula
a(n) = [x^n] (1+x)^(3*n+1)/(1-x)^(2*n+1).
a(n) = [x^n] 1/((1-x) * (1-2*x)^(2*n+1)).
a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(3*n+1,k).
a(n) = Sum_{k=0..n} 2^k * binomial(2*n+k,k).