A371787 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(5*n-k,n-2*k).
1, 5, 44, 441, 4675, 51129, 570401, 6451688, 73715212, 848793726, 9833394285, 114487194485, 1338411363535, 15700659542105, 184722993467063, 2178831068873601, 25756348168285379, 305061478075705411, 3619402085862708614, 43008294559624639777
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(5*n-k, n-2*k));
Formula
a(n) = [x^n] 1/((1-x+x^2) * (1-x)^(4*n)).
It appears that a(n) = Sum_{k = 0..n} binomial(3*n+2*k-1, k). - Peter Bala, Jun 04 2024