OFFSET
0,2
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 0..1001
Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015.
FORMULA
G.f.: (1-x)/(-x^2 + (1-x)*sqrt(1-4*x)); equivalently, the g.f. can be rewritten as -y^2*(y^2 - y + 1)/(y^4 - 3*y^3 + 4*y^2 - 4*y + 1), where y=A000108(x). - Gheorghe Coserea, Sep 10 2018
MATHEMATICA
om[n_] := om[n] = x om[n - 1] + Sum[(CatalanNumber[k - 1] x + 1) om[n - k], {k, 2, n}] // Expand; om[0] = 1; om[1] = x;
Array[om, 26, 0] /. x -> 2 (* Jean-François Alcover, Oct 25 2018 *)
PROG
(PARI)
A269750_seq(N, t='t) = {
my(a=vector(N), c(k)=binomial(2*k, k)/(k+1)); a[1]=1; a[2]=t;
for (n = 2, N-1,
a[n+1] = t*a[n] + sum(k = 2, n, (c(k-1)*t+1)*a[n+1-k]));
return(a);
};
A269750_seq(25, numdiv(2)) \\ Gheorghe Coserea, Sep 10 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 23 2016
EXTENSIONS
More terms from Gheorghe Coserea, Mar 24 2016
a(0)=1 prepended by Gheorghe Coserea, Sep 10 2018
STATUS
approved