|
%I #14 Mar 29 2024 15:21:39
%S 1,2,15,144,1587,18942,238301,3111788,41779164,573127760,7998164674,
%T 113189243386,1620583793262,23431706243230,341654376602948,
%U 5017986762425680,74170837061591036,1102479579201183898,16469074050937364044,247115476148847822586
%N G.f. satisfies A(x) = ( 1 + x*A(x)^3 * (1 + x*A(x)) )^2.
%F If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(s*k,n-k)/(t*k+u*(n-k)+r).
%o (PARI) a(n, r=2, s=1, t=6, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
%Y Cf. A000108, A143927, A365153, A368961, A371574.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 28 2024
|
