A365087 - OEIS

%I #12 Aug 21 2023 08:23:15

%S 1,1,-3,-1,29,-44,-265,1114,1369,-19076,20388,250977,-875281,-2116594,

%T 19136754,-7765108,-306092007,830209808,3388957208,-22266676364,

%U -8185922076,413223401045,-814031607979,-5513566634947,27558060911119,35395095404776

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n+3*k-1,n-k) / (n-k+1).

%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(n+3*k-1, n-k)/(n-k+1));

%Y Cf. A090192, A365085, A365086, A365088.

%Y Cf. A321798, A364737, A365083.

%K sign

%O 0,3

%A _Seiichi Manyama_, Aug 21 2023