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Search: id:A100642
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| A100642 |
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Triangle read by rows: numerators of Cotesian numbers C(n,k) (0 <= k <= k) if the denominators are set to the lcm's of the rows (A002176). |
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+0
2
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| 0, 1, 1, 1, 4, 1, 1, 3, 3, 1, 7, 32, 12, 32, 7, 19, 75, 50, 50, 75, 19, 41, 216, 27, 272, 27, 216, 41, 751, 3577, 1323, 2989, 2989, 1323, 3577, 751, 989, 5888, -928, 10496, -4540, 10496, -928, 5888, 989, 2857, 15741, 1080, 19344, 5778, 5778, 19344, 1080, 15741, 2857, 16067
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.
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EXAMPLE
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0, 1/2, 1/2, 1/6, 2/3, 1/6, 1/8, 3/8, 3/8, 1/8, 7/90, 16/45, 2/15, 16/45, 7/90, 19/288, 25/96, 25/144, 25/144, 25/96, 19/288, 41/840, 9/35, 9/280, 34/105, 9/280, 9/35, 41/840, ... = A100640/A100641 = A100642/A002176 (the latter is not in lowest terms)
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MAPLE
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(This defines the Cotesian numbers C(n, i)) with(combinat); C:=proc(n, i) if i=0 or i=n then RETURN( (1/n!)*add(n^a*stirling1(n, a)/(a+1), a=1..n+1) ); fi; (1/n!)*binomial(n, i)* add( add( n^(a+b)*stirling1(i, a)*stirling1(n-i, b)/((b+1)*binomial(a+b+1, b+1)), b=1..n-i+1), a=1..i+1); end;
den:=proc(n) local t1, i; t1:=1; for i from 0 to n do t1:=lcm(t1, denom(C(n, i))); od: t1; end; Then den(n)*C(n, k) gives the current sequence.
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CROSSREFS
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Cf. A100641, A100620, A100621, A002177, A002176, A100640.
Adjacent sequences: A100639 A100640 A100641 this_sequence A100643 A100644 A100645
Sequence in context: A016524 A087963 A010323 this_sequence A014518 A069289 A097322
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KEYWORD
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sign,frac
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AUTHOR
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njas, Dec 04 2004
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