A374675 a(n) = Sum_{k=0..n} binomial(n+k-1,n) * binomial(n+k,n).
1, 2, 21, 244, 3055, 40116, 544103, 7553960, 106734195, 1528937200, 22143771386, 323613807672, 4765050473521, 70611124679564, 1052084386116915, 15750153504353872, 236766112174722235, 3572264808332407512, 54073065371555283968, 820886646834780680640
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+k-1, n)*binomial(n+k, n));
Formula
a(n) = Sum_{k=0..n} (k/(n+k)) * binomial(n+k,k)^2 for n > 0.
a(n) = (n+1) * A259335(n).