A385671 - OEIS

A385671

a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(4*n+1,k) * binomial(4*n-k,n-k).

1, 22, 774, 30458, 1260886, 53731512, 2333065354, 102643195068, 4559878830006, 204091261040552, 9189096061165784, 415734554486178378, 18884084064916032026, 860673634902720476392, 39339618388269633525564, 1802605962076744803396888, 82777622289467318635747446

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) = [x^n] (1+2*x)^(4*n+1)/(1-3*x)^(3*n+1).

a(n) = [x^n] 1/((1-2*x) * (1-5*x)^(3*n+1)).

a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(4*n+1,k).

a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * binomial(3*n+k,k).

PROG

(PARI) a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(4*n+1, k)*binomial(4*n-k, n-k));