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Search: id:A100640
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| A100640 |
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Triangle read by rows: numerators of Cotesian numbers C(n,k) (0 <= k <= k). |
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+0
14
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| 0, 1, 1, 1, 2, 1, 1, 3, 3, 1, 7, 16, 2, 16, 7, 19, 25, 25, 25, 25, 19, 41, 9, 9, 34, 9, 9, 41, 751, 3577, 49, 2989, 2989, 49, 3577, 751, 989, 2944, -464, 5248, -454, 5248, -464, 2944, 989, 2857, 15741, 27, 1209, 2889, 2889, 1209, 27, 15741, 2857, 16067, 26575, -16175, 5675
(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
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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;
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CROSSREFS
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Cf. A100641-A100648, A100620, A100621, A002177, A002176.
Sequence in context: A026009 A137171 A010356 this_sequence A034929 A099509 A131336
Adjacent sequences: A100637 A100638 A100639 this_sequence A100641 A100642 A100643
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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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