A386867 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(4*n+2,k) * binomial(4*n-k-1,n-k).
1, 12, 249, 5842, 144636, 3690840, 96028606, 2532467934, 67454242092, 1810467982144, 48887478311673, 1326582594222918, 36143786784056716, 988134308856642048, 27093384379207568028, 744735869371387679158, 20516019688758402141372, 566266846186568482197840
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 2^(n-k)*binomial(4*n+2, k)*binomial(4*n-k-1, n-k));
Formula
a(n) = [x^n] (1+x)^(4*n+2)/(1-2*x)^(3*n).
a(n) = [x^n] 1/((1-x)^3 * (1-3*x)^(3*n)).
a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * binomial(4*n+2,k) * binomial(n-k+2,n-k).
a(n) = Sum_{k=0..n} 3^k * binomial(3*n+k-1,k) * binomial(n-k+2,n-k).