A100646 Denominator of Cotesian number C(n,2).

6, 8, 15, 144, 280, 640, 14175, 2240, 199584, 87091200, 875875, 22353408000, 5003856000, 229605376, 10854718875, 941525544960000, 1013940928000, 3064383995904000, 82324272054024, 2996771880960000, 255484332230400000, 809280523999877529600000, 5699209469078125

Offset

2,1

References

Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..200

Example

1/6, 3/8, 2/15, 25/144, 9/280, 49/640, -464/14175, 27/2240, -16175/199584, -3237113/87091200, -105387/875875, -1737125143/22353408000, -770720657/5003856000, -25881785/229605376, ... = A100645/A100646 = A002179/A002176 (the latter not being in lowest terms)

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}]; a[n_] := Denominator[cn[n, 2]]; Table[a[n], {n, 2, 24}]  (* Jean-François Alcover, Oct 08 2013 *)

Crossrefs

Cf. A100645.

See A002176 for further references. A diagonal of A100640/A100641.

Sequence in context: A022320 A318387 A349908 * A315927 A315928 A315929

Adjacent sequences: A100643 A100644 A100645 * A100647 A100648 A100649

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 05 2004

Status

approved