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A268538
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a(n) is the n-th prime 3-dimensional Catalan number.
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2
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1, 1, 2, 12, 107, 1178, 14805, 203885, 3002973, 46573347, 752521980, 12571607865, 215925120675, 3796546970232, 68106673339365, 1243210765414512, 23041656826384341
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OFFSET
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0,3
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COMMENTS
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"Prime" here is used in the sense of "primitive" or "irreducible".
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LINKS
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FORMULA
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Lemma 15 of Wettstein (2016) gives a formula in terms of the 3-dimensional Catalan numbers (A005789).
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MAPLE
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2*(3*n)!/(n+2)!/(n+1)!/n! ;
end proc:
maxn := 30 :
Cx := add(A005789(i)*x^i, i=0..maxn) ;
d := 3:
for i from 0 to maxn do
coeftayl(1/Cx^(d*i-1), x=0, i) ;
%/(1-d*i) ;
printf("%d, ", %) ;
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MATHEMATICA
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A005789[n_] := 2*(3*n)!/(n+2)!/(n+1)!/n!; Maxn = 30; Cx = Sum[A005789[i]* x^i, {i, 0, Maxn}]; d = 3; Reap[For[i = 0, i <= Maxn, i++, sc = SeriesCoefficient[1/Cx^(d*i-1), {x, 0, i}]; Sow[sc/(1-d*i)]]][[2, 1]] (* Jean-François Alcover, Mar 24 2018, after R. J. Mathar *)
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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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