A364866 - OEIS

%I #15 Aug 26 2023 18:17:25

%S 1,1,4,21,124,781,5120,34474,236492,1644222,11543644,81623504,

%T 580104672,4137414963,29574658416,211639869236,1514729242092,

%U 10832683182538,77342204972120,550791674067623,3908735530965604,27612614422978557,193943797650498016

%N G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^5).

%C a(34) is negative.

%H Seiichi Manyama, <a href="/A364866/b364866.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(n,k) * binomial(5*n+k+1,n) / (5*n+k+1).

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

%F a(n) = (1/n) * Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * binomial(5*n,k-1) for n > 0.

%o (PARI) a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(5*n+k+1, n)/(5*n+k+1));

%Y Cf. A291534, A364864, A364865, A365218.

%Y Cf. A002295.

%K sign

%O 0,3

%A _Seiichi Manyama_, Aug 11 2023