A371581 - OEIS

%I #17 Mar 29 2024 15:21:31

%S 1,2,13,108,1018,10352,110724,1227752,13986369,162708728,1924866345,

%T 23085868814,280060995369,3430479393210,42369377446083,

%U 527064922683286,6597825455023465,83050276697808472,1050551595788997356,13347641275527720048,170259412138463630535

%N G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (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(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).

%F G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A365192.

%o (PARI) a(n, r=2, s=1, t=5, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

%Y Cf. A006013, A211789, A365146, A371582.

%Y Cf. A371574, A365192.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 28 2024