A386868 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(2*n+2,k) * binomial(2*n-k,n-k).
1, 8, 75, 760, 8030, 87036, 959623, 10710320, 120635550, 1368461440, 15611831774, 178932199152, 2058727445320, 23764328143220, 275083791201375, 3191938947518560, 37116092204482550, 432393735569959440, 5045632228616597290, 58965061323736782800, 690005032437397594260
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 2^(n-k)*binomial(2*n+2, k)*binomial(2*n-k, n-k));
Formula
a(n) = [x^n] (1+x)^(2*n+2)/(1-2*x)^(n+1).
a(n) = [x^n] 1/((1-x)^2 * (1-3*x)^(n+1)).
a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * (n-k+1) * binomial(2*n+2,k).
a(n) = Sum_{k=0..n} 3^k * (n-k+1) * binomial(n+k,k).