A364765 - OEIS

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A364765

G.f. A(x) satisfies A(x) = 1 + x*A(x)^4 / (1 - x*A(x)^5).

1, 1, 5, 36, 304, 2808, 27475, 279845, 2935987, 31511097, 344344868, 3818320487, 42855633210, 485923475563, 5557803724920, 64046876264292, 742908320701832, 8667090253409215, 101631581618367133, 1197190915359577973, 14160413911721178800

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..909

FORMULA

G.f. satisfies A(x) = 1 + x*A(x)^6 / (1 + x*A(x)^4).

a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(4*n+k,n-1-k) for n > 0.

a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * binomial(6*n-2*k,n-1-k) for n > 0.

a(n) = (1/n) * Sum_{k=0..floor(n-1)/2} binomial(n,k) * binomial(5*n-k,n-1-2*k) for n > 0. - Seiichi Manyama, Apr 01 2024

PROG

(PARI) a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(4*n+k, n-1-k))/n);