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A270785
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Number of Schur rings over Z_{3^n}.
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4
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1, 2, 7, 25, 92, 345, 1311, 5030, 19439, 75545, 294888, 1155205, 4538745, 17876250, 70553179, 278949705, 1104585634, 4379770585, 17386456213, 69090680674, 274806384941, 1093933313537, 4357881016922, 17371974200097, 69292334180593, 276541159696582
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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MATHEMATICA
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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;
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PROG
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(PARI)
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);
};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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