A378686 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(7/3)/(1 - x*A(x)) )^3.

1, 3, 27, 313, 4122, 58584, 875897, 13577139, 216224616, 3516601243, 58160887857, 975211608399, 16539799297342, 283243124783136, 4890858070498203, 85060240453556192, 1488653675438168001, 26197808077514204832, 463311206395709908936, 8229849868810254813378

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^2/(1 - x*A(x)) )^3.

G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A378685.

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).

Prog

(PARI) a(n, r=3, s=1, t=7, u=3) = 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));

Crossrefs

Cf. A108447, A371581.

Cf. A349017, A369012.

Cf. A378690, A378692, A378693.

Cf. A378685.

Sequence in context: A318108 A290576 A291315 * A364965 A078532 A264684

Adjacent sequences: A378681 A378682 A378685 * A378687 A378688 A378690

Keyword

nonn,new

Author

Seiichi Manyama, Dec 04 2024

Status

approved