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A156282
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Irregular triangle read by rows: row n is the expansion of the product of cyclotomic polynomials from 2nd to n-th polynomial.
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1
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1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 3, 2, 1, 1, 3, 6, 9, 11, 11, 9, 6, 3, 1, 1, 2, 4, 6, 8, 9, 9, 8, 6, 4, 2, 1, 1, 3, 7, 13, 21, 30, 39, 46, 50, 50, 46, 39, 30, 21, 13, 7, 3, 1, 1, 3, 7, 13, 22, 33, 46, 59, 71, 80, 85, 85, 80, 71, 59, 46, 33, 22, 13, 7, 3, 1, 1, 3, 7, 14, 25, 40, 60, 84, 111, 139
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OFFSET
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0,6
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LINKS
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EXAMPLE
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1;
1;
1, 1;
1, 2, 2, 1;
1, 2, 3, 3, 2, 1;
1, 3, 6, 9, 11, 11, 9, 6, 3, 1;
1, 2, 4, 6, 8, 9, 9, 8, 6, 4, 2, 1;
1, 3, 7, 13, 21, 30, 39, 46, 50, 50, 46, 39, 30, 21, 13, 7, 3, 1;
1, 3, 7, 13, 22, 33, 46, 59, 71, 80, 85, 85, 80, 71, 59, 46, 33, 22, 13, 7, 3, 1;
1, 3, 7, 14, 25, 40, 60, 84, 111, 139, 166, 189, 206, 215, 215, 206, 189, 166, 139, 111, 84, 60, 40, 25, 14, 7, 3, 1
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MAPLE
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T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(
mul(numtheory[cyclotomic](i, x), i=2..n)):
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MATHEMATICA
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row[n_] := CoefficientList[Product[Cyclotomic[k+1, x], {k, 1, n}], x];
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PROG
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(PARI) row(n) = Vec(prod(k=1, n, polcyclo(k+1))); \\ Michel Marcus, Dec 12 2017
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CROSSREFS
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Cf. A002088 (row lengths for n>=1).
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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