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

%I

%S 2,2,4,2,12,8,2,28,48,16,2,60,200,160,32,2,124,720,1040,480,64,2,252,

%T 2408,5600,4480,1344,128,2,508,7728,27216,33600,17024,3584,256,2,1020,

%U 24200,124320,222432,169344,59136,9216,512,2,2044,74640,545680,1360800,1460928,752640,192000,23040,1024

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

%C 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.

%C 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

%C 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

%H Indranil Ghosh, <a href="/A227450/b227450.txt">Rows 1..125, flattened</a>

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

%e 2,

%e 2, 4,

%e 2, 12, 8,

%e 2, 28, 48, 16,

%e 2, 60, 200, 160, 32,

%e 2, 124, 720, 1040, 480, 64

%t 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

%t (* or *)

%t Flatten[Table[StirlingS2[n,k]*2^k,{n,1,10},{k,1,n}]] (* _Indranil Ghosh_, Feb 22 2017 *)

%t BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];

%t B = BellMatrix[2&, rows = 12];

%t Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* _Jean-François Alcover_, Jun 28 2018, after _Peter Luschny_ *)

%o # The function BellMatrix is defined in A264428.

%o # Adds (1,0,0,0, ..) as column 0.

%o BellMatrix(n -> 2, 9); # _Peter Luschny_, Jan 29 2016

%Y Cf. A008277.

%K nonn,tabl

%O 1,1

%A _Geoffrey Critzer_, Sep 22 2013

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Last modified July 31 22:17 EDT 2021. Contains 346377 sequences. (Running on oeis4.)