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A100640
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Triangle read by rows: numerators of Cotesian numbers C(n,k) (0 <= k <= n).
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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; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.
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EXAMPLE
| 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
| (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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MATHEMATICA
| a[n_, i_] /; i == 0 || i == n = 1/n! Sum[n^a*StirlingS1[n, a]/(a + 1), {a, 1, n + 1}]; a[n_, i_] = 1/n!*Binomial[n, i]*Sum[ n^(a + b)*StirlingS1[i, a]*StirlingS1[n - i, b]/((b + 1)*Binomial[a + b + 1, b + 1]), {b, 1, n}, {a, 1, i + 1}]; Table[a[n, i], {n, 0, 10}, {i, 0, n}] // Flatten // Numerator // Take[#, 59]&
(* From Jean-François Alcover, May 17 2011, after Maple prog. *)
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CROSSREFS
| Cf. A100641-A100648, A100620, A100621, A002177, A002176.
Sequence in context: A026009 A137171 A010356 * A175424 A144401 A034929
Adjacent sequences: A100637 A100638 A100639 * A100641 A100642 A100643
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KEYWORD
| sign,frac,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2004
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