A370104 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n+k-1,k) * binomial(6*n-k-1,n-k).
1, 3, 25, 219, 2025, 19253, 186469, 1829565, 18124521, 180886260, 1815946275, 18318160358, 185518492965, 1885157971596, 19211066004995, 196258973605094, 2009302383218409, 20610411795602760, 211768072490024440, 2179156980022097775, 22454554231950998275
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-1)^k*binomial(2*n+k-1, k)*binomial(6*n-k-1, n-k));
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PARI
a(n, s=2, t=2, 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)^2 * (1-x)^5 )^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)^2*(1-x)^5 ). See A365856.
a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(4*n-2*k-1,n-2*k).