A370105 a(n) = Sum_{k=0..n} (-1)^k * binomial(n+k-1,k) * binomial(5*n-k-1,n-k).
1, 3, 23, 192, 1687, 15253, 140504, 1311292, 12357015, 117318162, 1120436273, 10752242592, 103596191608, 1001494496863, 9709576926716, 94369011385192, 919175964169623, 8970063281146830, 87685232945278010, 858446087522807784, 8415669293820893937
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-1)^k*binomial(n+k-1, k)*binomial(5*n-k-1, n-k));
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PARI
a(n, s=2, t=1, u=3) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));
Formula
a(n) = [x^n] 1/( (1+x) * (1-x)^4 )^n.
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x*(1+x)*(1-x)^4 ). See A365752.
a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1,k) * binomial(4*n-2*k-1,n-2*k).