A378920 G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)^2).

1, 1, 5, 38, 339, 3308, 34191, 367844, 4076112, 46204209, 533239820, 6244542391, 74016115926, 886276231388, 10704869669941, 130271156244371, 1595708949486866, 19658780721376791, 243429900033986385, 3028086095940468087, 37821457123957529163, 474145963420441744445

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)^2)).

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=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));

Crossrefs

Cf. A002294, A349362, A364765, A365218, A378892, A378919.

Cf. A000108, A219537, A291534, A365225.

Sequence in context: A207411 A316598 A228657 * A370476 A369480 A365839

Adjacent sequences: A378917 A378918 A378919 * A378921 A378922 A378923

Keyword

nonn

Author

Seiichi Manyama, Dec 11 2024

Status

approved