%I #11 Oct 09 2013 14:09:27

%S 6,8,15,144,280,640,14175,2240,199584,87091200,875875,22353408000,

%T 5003856000,229605376,10854718875,941525544960000,1013940928000,

%U 3064383995904000,82324272054024,2996771880960000,255484332230400000,809280523999877529600000,5699209469078125

%N Denominator of Cotesian number C(n,2).

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

%H Vincenzo Librandi, <a href="/A100646/b100646.txt">Table of n, a(n) for n = 2..200</a>

%e 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)

%t 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 *)

%Y Cf. A100645.

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

%K nonn,frac

%O 2,1

%A _N. J. A. Sloane_, Dec 05 2004