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Search: id:A059836
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| A059836 |
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Triangle T(s,t), s>=1, 1<=t<=s (see formula line). |
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+0
2
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| 1, 1, 1, 1, 2, 4, 1, 3, 9, 18, 1, 4, 16, 48, 144, 1, 5, 25, 100, 400, 1200, 1, 6, 36, 180, 900, 3600, 14400, 1, 7, 49, 294, 1764, 8820, 44100, 176400, 1, 8, 64, 448, 3136, 18816, 112896, 564480, 2822400, 1, 9, 81, 648, 5184, 36288, 254016, 1524096, 9144576
(list; table; graph; listen)
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OFFSET
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1,5
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REFERENCES
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S. G. Mikhlin, Constants in Some Inequalities of Analysis, Wiley, NY, 1986, see p. 59.
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FORMULA
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T(s, t) = (s-1)^2*(s-2)^2*...(s-(t-1)/2)^2 if t odd, else (s-1)^2*(s-2)^2*...(s-t/2+1)^2*(s-t/2).
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EXAMPLE
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1; 1,1; 1,2,4; 1,3,9,18; ...
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MAPLE
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T := proc(s, t) option remember: if s=1 or t=1 then RETURN(1) fi: if t>1 and t mod 2 = 1 then RETURN(product((s-i)^2, i=1..(t-1)/2)) else RETURN((s-t/2)*product((s-i)^2, i=1..t/2-1)) fi: end: for s from 1 to 15 do for t from 1 to s do printf(`%d, `, T(s, t)) od:od:
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CROSSREFS
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Cf. A059837.
Sequence in context: A011233 A076053 A100075 this_sequence A069270 A079901 A121426
Adjacent sequences: A059833 A059834 A059835 this_sequence A059837 A059838 A059839
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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njas, Feb 25 2001
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 26 2001, and from Larry Reeves (larryr(AT)acm.org), Feb 26 2001.
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