A378733 G.f. A(x) satisfies A(x) = 1 + x / (1 - x*A(x)^2)^4.

1, 1, 4, 18, 96, 551, 3332, 20906, 134820, 888151, 5951096, 40432550, 277892604, 1928668910, 13497833600, 95150192558, 674993798716, 4815149310441, 34519885929860, 248571425473698, 1797058507267104, 13038781500215352, 94914559729835580, 692987915940266152

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: A(x) = sqrt(B(x)) where B(x) is the g.f. of A365123.

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=1, s=4, t=0, 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));

Crossrefs

Cf. A001764, A161634, A367236.

Cf. A365123.

Sequence in context: A243325 A005777 A180567 * A152392 A001563 A094304

Adjacent sequences: A378730 A378731 A378732 * A378735 A378736 A378737

Keyword

nonn,new

Author

Seiichi Manyama, Dec 06 2024

Status

approved