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A162299
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Triangle T(k,y) read by rows: denominator of the coefficient [m^y] of the polynomial sum_{x=1..m} x^(k-1).
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4
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1, 2, 2, 6, 2, 3, 1, 4, 2, 4, 30, 1, 3, 2, 5, 1, 12, 1, 12, 2, 6, 42, 1, 6, 1, 2, 2, 7, 1, 12, 1, 24, 1, 12, 2, 8, 30, 1, 9, 1, 15, 1, 3, 2, 9, 1, 20, 1, 2, 1, 10, 1, 4, 2, 10, 66, 1, 2, 1, 1, 1, 1, 1, 6, 2, 11, 1, 12, 1, 8, 1, 6, 1, 8, 1, 12, 2, 12, 2730, 1, 3, 1, 10, 1, 7, 1, 6, 1, 1, 2, 13, 1, 420, 1, 12, 1, 20, 1, 28, 1, 60, 1, 12, 2, 14, 6, 1, 90, 1, 6, 1, 10, 1, 18, 1, 30, 1, 6, 2, 15
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| sum_{x=1..m} x^(k-1) = (Bernoulli(k,m+1)-Bernoulli(k))/k.
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EXAMPLE
| (See A162298 for the fractions).
The triangle starts in row k=1 with columns 1<=y<=k as
1
2 2
6 2 3
1 4 2 4
30 1 3 2 5
1 12 1 12 2 6
42 1 6 1 2 2 7
1 12 1 24 1 12 2 8
30 1 9 1 15 1 3 2 9
1 20 1 2 1 10 1 4 2 10
66 1 2 1 1 1 1 1 6 2 11
1 12 1 8 1 6 1 8 1 12 2 12
2730 1 3 1 10 1 7 1 6 1 1 2 13
1 420 1 12 1 20 1 28 1 60 1 12 2 14
6 1 90 1 6 1 10 1 18 1 30 1 6 2 15
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MAPLE
| A162299 := proc(k, y) local gf, x; gf := sum(x^(k-1), x=1..m) ; coeftayl(gf, m=0, y) ; denom(%) ; end proc: # R. J. Mathar, Jan 24 2011
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CROSSREFS
| Cf. A000027, A000367, A162298 (numerators), A053382, A053383.
Sequence in context: A126889 A205030 A134339 * A205506 A110141 A129750
Adjacent sequences: A162296 A162297 A162298 * A162300 A162301 A162302
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KEYWORD
| nonn,tabl,frac
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AUTHOR
| Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 30 2009
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EXTENSIONS
| Corrected by Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 02 2009
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