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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 (list; graph; refs; listen; history; text; internal format)
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.: 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-Fran├žois 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

Cf. A000108, A269750.

Sequence in context: A151225 A326984 A296771 * A151226 A151320 A151227

Adjacent sequences:  A270783 A270784 A270785 * A270787 A270788 A270789

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

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Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)