A371581 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x*A(x)) )^2.

1, 2, 13, 108, 1018, 10352, 110724, 1227752, 13986369, 162708728, 1924866345, 23085868814, 280060995369, 3430479393210, 42369377446083, 527064922683286, 6597825455023465, 83050276697808472, 1050551595788997356, 13347641275527720048, 170259412138463630535

Offset: 0

Author

Seiichi Manyama, Mar 28 2024

Keywords

• nonn

Crossrefs

Cf. A006013, A211789, A365146, A371582.

Cf. A371574, A365192.

Programs

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));

Formula

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).

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