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Search: id:A100620
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| A100620 |
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Numerator of Cotesian number C(n,0). |
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+0
9
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| 0, 1, 1, 1, 7, 19, 41, 751, 989, 2857, 16067, 434293, 1364651, 8181904909, 90241897, 5044289, 15043611773, 5026792806787, 203732352169, 69028763155644023, 1145302367137, 1022779523247467, 396760150748100749, 750218743980105669781, 35200969735190093
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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, 1/6, 1/8, 7/90, 19/288, 41/840, 751/17280, 989/28350, 2857/89600, 16067/598752, 434293/17418240, 1364651/63063000, 8181904909/402361344000, ... = A100620/A100621 = A002177/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;
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CROSSREFS
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See A002176 for further references. A diagonal of A100640/A100641.
Adjacent sequences: A100617 A100618 A100619 this_sequence A100621 A100622 A100623
Sequence in context: A097240 A097241 A067889 this_sequence A002177 A141193 A104163
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KEYWORD
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nonn,frac
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AUTHOR
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njas, Dec 04 2004
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