A378892 G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)^3).

1, 1, 5, 37, 322, 3067, 30951, 325171, 3519038, 38959997, 439177850, 5023590609, 58163050071, 680308820750, 8026782091957, 95419476630100, 1141762194395927, 13740910664096101, 166216043531507231, 2019807368837970964, 24644779751103948475, 301818330734940817283

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^5/(1 + x*A(x)^3)).

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).

Prog

(PARI) a(n, r=1, s=-1, t=6, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A001764, A271469, A363982, A364736, A364864.

Cf. A378891.

Sequence in context: A176818 A359643 A068785 * A199562 A246540 A365842

Adjacent sequences: A378889 A378890 A378891 * A378893 A378894 A378897

Keyword

nonn,new

Author

Seiichi Manyama, Dec 10 2024

Status

approved