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 A227450 Triangular array read by rows. T(n,k) = A008277(n,k)*2^k; n >= 1, 1 <= k <= n. 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 # The function BellMatrix is defined in A264428. # Adds (1, 0, 0, 0, ..) as column 0. BellMatrix(n -> 2, 9); # Peter Luschny, Jan 29 2016 CROSSREFS Cf. A008277. Sequence in context: A067228 A332002 A229756 * A010026 A059427 A137777 Adjacent sequences:  A227447 A227448 A227449 * A227451 A227452 A227453 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Sep 22 2013 STATUS approved

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Last modified June 18 04:41 EDT 2021. Contains 345098 sequences. (Running on oeis4.)