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

1,1

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

Cf. A008277.

Sequence in context: A356543 A332002 A229756 * A010026 A059427 A137777

Adjacent sequences: A227447 A227448 A227449 * A227451 A227452 A227453

Keyword

nonn,tabl

Author

Geoffrey Critzer, Sep 22 2013

Status

approved