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A270786
Number of Schur rings over Z_{5^n}.
4
1, 3, 13, 58, 263, 1203, 5531, 25511, 117910, 545730, 2528263, 11720917, 54364253, 252243996, 1170694877, 5434421231, 25230661483, 117153235821, 544024844668, 2526465046405, 11733602605442, 54496414141998, 253115681845187, 1175659969364675, 5460766440081739
OFFSET
0,2
LINKS
Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015.
FORMULA
G.f.: 2*(1-x)/(-2*x^2 + (x-1) + 3*(1-x)*sqrt(1-4*x)); equivalently, the g.f. can be rewritten as -y^2*(y^2 - y + 1)/(2*y^4 - 5*y^3 + 6*y^2 - 5*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, 25, 0] /. x -> 3 (* 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(4)) \\ Gheorghe Coserea, Sep 10 2018
CROSSREFS
Sequence in context: A151225 A326984 A296771 * A151226 A151320 A151227
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