A378919 G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)).

1, 1, 5, 39, 355, 3532, 37206, 407861, 4604493, 53169811, 625067441, 7456004083, 90015754691, 1097834790182, 13505674728174, 167395320811562, 2088350145491232, 26203315734195937, 330460721192844017, 4186559092558049570, 53255890990455126082, 679954025388880445771

Offset: 0

Author

Seiichi Manyama, Dec 11 2024

Keywords

• nonn

Crossrefs

Cf. A002294, A349362, A364765, A365218, A378892, A378920.

Cf. A106228, A364758, A364759.

Programs

PARI

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

Formula

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

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).