A386837 a(n) = Sum_{k=0..n} binomial(4*n+2,k) * binomial(4*n-k-1,n-k).
1, 9, 126, 1978, 32703, 556887, 9665476, 170006256, 3019802253, 54047520709, 973141183002, 17607177876438, 319855973830251, 5830329608105763, 106583422441886592, 1953315343946213804, 35875864591309216089, 660185366847433991025, 12169379986275311820790
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(4*n+2, k)*binomial(4*n-k-1, n-k));
Formula
a(n) = [x^n] (1+x)^(4*n+2)/(1-x)^(3*n).
a(n) = [x^n] 1/((1-x)^3 * (1-2*x)^(3*n)).
a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(4*n+2,k) * binomial(n-k+2,n-k).
a(n) = Sum_{k=0..n} 2^k * binomial(3*n+k-1,k) * binomial(n-k+2,n-k).