A386862 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(2*n+1,k) * binomial(2*n-k-1,n-k).
1, 5, 42, 409, 4238, 45414, 496996, 5517929, 61909878, 700189606, 7968994124, 91158632250, 1047156227068, 12071222381456, 139569181458552, 1617879480097129, 18796461329347238, 218806784598226926, 2551538498649588892, 29800118958422522414, 348529038403155280548
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 2^(n-k)*binomial(2*n+1, k)*binomial(2*n-k-1, n-k));
Formula
a(n) = [x^n] (1+x)^(2*n+1)/(1-2*x)^n.
a(n) = [x^n] 1/((1-x)^2 * (1-3*x)^n).
a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * (n-k+1) * binomial(2*n+1,k).
a(n) = Sum_{k=0..n} 3^k * (n-k+1) * binomial(n+k-1,k).