This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A100641 Triangle read by rows: denominators of Cotesian numbers C(n,k) (0 <= k <= k). 16
 1, 2, 2, 6, 3, 6, 8, 8, 8, 8, 90, 45, 15, 45, 90, 288, 96, 144, 144, 96, 288, 840, 35, 280, 105, 280, 35, 840, 17280, 17280, 640, 17280, 17280, 640, 17280, 17280, 28350, 14175, 14175, 14175, 2835, 14175, 14175, 14175, 28350, 89600, 89600, 2240, 5600, 44800, 44800, 5600 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513. L. M. Milne-Thompson, Calculus of Finite Differences, MacMillan, 1951, p. 170. LINKS EXAMPLE Triangle A100640/A100641 begins: [1], [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], [751/17280, 3577/17280, 49/640, 2989/17280, 2989/17280, 49/640, 3577/17280, 751/17280], ... 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; # Another program: T:=proc(n, k) (-1)^(n-k)*(n/(n-1))*binomial(n-1, k-1)* integrate(expand(binomial(t-1, n))/(t-k), t=1..n); end; [[1], seq( [seq(T(n, k), k=1..n)], n=2..14)]; 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 // Denominator // Take[#, 52] & (* Jean-François Alcover, May 17 2011, after Maple prog. *) CROSSREFS Cf. A100640-A100648, A100620, A100621, A002177, A002176. Sequence in context: A085738 A227608 A276484 * A028421 A263003 A081745 Adjacent sequences:  A100638 A100639 A100640 * A100642 A100643 A100644 KEYWORD nonn,frac,tabl AUTHOR N. J. A. Sloane, Dec 04 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.