A386864 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(4*n+1,k) * binomial(4*n-k-1,n-k).
1, 11, 228, 5350, 132476, 3380955, 87974188, 2320223552, 61804459260, 1658904186124, 44796539697968, 1215611557398534, 33121179085639252, 905520072985022570, 24828701435772435528, 682496748843439692868, 18801742541632193099996, 518957827806105486222372
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 2^(n-k)*binomial(4*n+1, k)*binomial(4*n-k-1, n-k));
Formula
a(n) = [x^n] (1+x)^(4*n+1)/(1-2*x)^(3*n).
a(n) = [x^n] 1/((1-x)^2 * (1-3*x)^(3*n)).
a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * (n-k+1) * binomial(4*n+1,k).
a(n) = Sum_{k=0..n} 3^k * (n-k+1) * binomial(3*n+k-1,k).