%I #12 Sep 20 2024 12:27:52

%S 1,4,26,200,1691,15180,142038,1370076,13526645,136024876,1388394234,

%T 14346699052,149790104030,1577765967600,16745718467070,

%U 178912981116840,1922688816819276,20769064846817136,225384498769815750,2455985319885345820,26862562977746930145,294807644917408047060

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

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F If g.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x))^s)^t, then a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(t*(n+1),k) * binomial(s*k,n-k).

%F G.f.: (1/x) * Series_Reversion( x / (1+x+x^2)^4 ).

%F G.f.: B(x)^4, where B(x) is the g.f. of A365183.

%o (PARI) a(n, s=1, t=4) = sum(k=0, n, binomial(t*(n+1), k)*binomial(s*k, n-k))/(n+1);

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^2)^4)/x)

%Y Cf. A143927, A365128, A376328.

%Y Cf. A365183.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 20 2024