A386845 a(n) = Sum_{k=0..n} binomial(4*n+2,k) * binomial(4*n-k,n-k).
1, 10, 143, 2264, 37601, 642086, 11165395, 196658228, 3496849349, 62636490818, 1128525823927, 20429545554000, 371294468833193, 6770529284259934, 123811606398566299, 2269695135303598188, 41697091253148057485, 767476182916622450810, 14149874243880085356415
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(4*n+2, k)*binomial(4*n-k, n-k));
Formula
a(n) = [x^n] (1+x)^(4*n+2)/(1-x)^(3*n+1).
a(n) = [x^n] 1/((1-x)^2 * (1-2*x)^(3*n+1)).
a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * (n-k+1) * binomial(4*n+2,k).
a(n) = Sum_{k=0..n} 2^k * (n-k+1) * binomial(3*n+k,k).