A227450 Triangular array read by rows. T(n,k) = A008277(n,k)*2^k; n >= 1, 1 <= k <= n.

2, 2, 4, 2, 12, 8, 2, 28, 48, 16, 2, 60, 200, 160, 32, 2, 124, 720, 1040, 480, 64, 2, 252, 2408, 5600, 4480, 1344, 128, 2, 508, 7728, 27216, 33600, 17024, 3584, 256, 2, 1020, 24200, 124320, 222432, 169344, 59136, 9216, 512, 2, 2044, 74640, 545680, 1360800, 1460928, 752640, 192000, 23040, 1024

Offset: 1

Author

Geoffrey Critzer, Sep 22 2013

Keywords

• nonn
• tabl

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

Examples

			2,
2, 4,
2, 12, 8,
2, 28, 48, 16,
2, 60, 200, 160, 32,
2, 124, 720, 1040, 480, 64
		

Links

• Indranil Ghosh, Rows 1..125, flattened

Crossrefs

Cf. A008277.

Programs

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 *)

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

Formula

E.g.f.: A(x,y)^2 where A(x,y) is the e.g.f. for A008277.