A365180 - OEIS

%I #9 Aug 25 2023 09:43:22

%S 1,1,5,31,223,1740,14328,122549,1078197,9695359,88710199,823247686,

%T 7730244098,73310150097,701163085849,6755544043969,65506554804129,

%U 638794412442172,6260571309256152,61632794482411367,609197871548209907,6043456939539775056

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

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

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

%Y Cf. A002294, A365178, A365181, A365182, A365183.

%Y Cf. A364747.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 25 2023