%I #10 Sep 20 2024 12:27:57
%S 1,5,40,380,3970,44051,509575,6077435,74194780,922644310,11646083631,
%T 148827827450,1921724362880,25034267112600,328614891689845,
%U 4342322118727300,57715241768897445,771087466276360970,10349495416322497575,139486475071720234920,1886980259513934080860,25613816043115261657425
%N G.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x)))^5.
%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)^5 ).
%F G.f.: B(x)^5, where B(x) is the g.f. of A365189.
%o (PARI) a(n, s=1, t=5) = 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)^5)/x)
%Y Cf. A143927, A365128, A376320.
%Y Cf. A365189.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Sep 20 2024