OFFSET
1,1
COMMENTS
T(n,k) is the number of ways to separate {1,2,...,n} into 2 ordered subsets S,T so that the union of S and T = {1,2,...,n} then partition each subset so that the total number of blocks over both subsets is equal to k.
Triangle T(n,k), 1<=k<=n, read by rows, given by (0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, ...) DELTA (2, 0, 2, 0, 2, 0, 2, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Sep 23 2013
Also the Bell transform of the constant sequence "a(n) = 2". For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016
LINKS
Indranil Ghosh, Rows 1..125, flattened
FORMULA
E.g.f.: A(x,y)^2 where A(x,y) is the e.g.f. for A008277.
EXAMPLE
2,
2, 4,
2, 12, 8,
2, 28, 48, 16,
2, 60, 200, 160, 32,
2, 124, 720, 1040, 480, 64
MATHEMATICA
nn=8; a=Exp[x]-1; Map[Select[#, #>0&]&, Drop[Range[0, nn]! CoefficientList[Series[Exp[y a]^2, {x, 0, nn}], {x, y}], 1]]//Grid
(* or *)
Flatten[Table[StirlingS2[n, k]*2^k, {n, 1, 10}, {k, 1, n}]] (* Indranil Ghosh, Feb 22 2017 *)
BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
B = BellMatrix[2&, rows = 12];
Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jun 28 2018, after Peter Luschny *)
PROG
(Python) # The function BellMatrix is defined in A264428.
# Adds (1, 0, 0, 0, ..) as column 0.
BellMatrix(lambda n: 2, 9); # Peter Luschny, Jan 29 2016
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Sep 22 2013
STATUS
approved