3,2

Those numbers (4, 20, 120, 840, 6720, ..., ) arise from the divisor values in the general formula a(n)=n*(n+1)*(n+2)*(n+3)* ...* (n+k) *(n*(n+k) + (k-1)*k/6)/((k+3)!/6) (which covers following sequences: A000578, A000537, A024166, A101094, A101097, A101102) - Alexander R. Povolotsky (pevnev(AT)juno.com), May 17 2008

Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Index entries for sequences related to factorial numbers

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 263

Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7

E.g.f. if offset 0: 1/(1-x)^4.

f := proc(n) n!/6; end;

seq(mul((k), k=4..n), n=3..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 14 2007

a[0]:=1:a[1]:=1:for n from 2 to 50 do a[n]:=(a[n-1]*(n+2)^2) od: seq(sqrt(a[n]), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 04 2008

BB:= [S, {S = Prod(Z, Z, C), C = Union(B, Z, Z), B = Prod(Z, C)}, labelled]: seq(combstruct[count](BB, size=n)/12, n=3..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 19 2008

a:=n->mul(denom((k+1)/(k+2) ), k=2..n): seq(a(n), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 02 2008

a:=n->mul(numer((k+1)/(k+2) ), k=3..n): seq(a(n), n=2..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 02 2008

a(n) = A049352(n-2, 1) (first column of triangle). Cf. A049458, A049460.

Cf. A034472.

Sequence in context: A046729 A093123 A092055 this_sequence A020028 A020118 A009351

Adjacent sequences: A001712 A001713 A001714 this_sequence A001716 A001717 A001718

nonn,easy

njas