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A100620 Numerator of Cotesian number C(n,0). 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
REFERENCES
Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.
LINKS
EXAMPLE
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)
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;
MATHEMATICA
cn[n_, 0] := Sum[n^j*StirlingS1[n, j]/(j + 1), {j, 1, n + 1}]/n!; cn[n_, n_] := cn[n, 0]; cn[n_, k_] := 1/n!*Binomial[n, k]*Sum[n^(j + m)*StirlingS1[k, j]*StirlingS1[n - k, m]/((m + 1)*Binomial[j + m + 1, m + 1]), {m, 1, n}, {j, 1, k + 1}]; Table[cn[n, 0] // Numerator, {n, 0, 24}] (* Jean-François Alcover, Jan 16 2013 *)
CROSSREFS
See A002176 for further references. A diagonal of A100640/A100641.
Sequence in context: A097241 A067889 A190821 * A002177 A225279 A192755
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Dec 04 2004
STATUS
approved

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Last modified February 26 10:35 EST 2024. Contains 370346 sequences. (Running on oeis4.)