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 A130123 Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Triangle by columns, (2^k, 0, 0, 0, ...). 8
 1, 0, 2, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4096 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A 2^n transform matrix. A130123 * A007318 = A038208. A007318 * A130123 = A013609. A130124 = A130123 * A002260. A130125 = A128174 * A130123. Triangle T(n,k), 0 <= k <= n, given by [0,0,0,0,0,0,...] DELTA [2,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, May 26 2007 Also the Bell transform of A000038. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 27 2016 LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened FORMULA G.f.: 1/(1-2*x*y). - R. J. Mathar, Aug 11 2015 EXAMPLE First few terms of the triangle:   1;   0, 2;   0, 0, 4;   0, 0, 0, 8;   0, 0, 0, 0, 16;   0, 0, 0, 0,  0, 32; ... MAPLE # The function BellMatrix is defined in A264428. BellMatrix(n -> `if`(n=0, 2, 0), 9); # Peter Luschny, Jan 27 2016 MATHEMATICA BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]]; rows = 12; M = BellMatrix[If[# == 0, 2, 0]&, rows]; Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 23 2018, after Peter Luschny *) Table[If[k==n, 2^n, 0], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 05 2019 *) PROG (PARI) {T(n, k) = if(k==n, 2^n, 0)}; \\ G. C. Greubel, Jun 05 2019 (MAGMA) [[k eq n select 2^n else 0: k in [0..n]]: n in [0..14]]; // G. C. Greubel, Jun 05 2019 (Sage) def T(n, k):     if (k==n): return 2^n     else: return 0 [[T(n, k) for k in (0..n)] for n in (0..14)] # G. C. Greubel, Jun 05 2019 CROSSREFS Cf. A130124, A130125. Sequence in context: A028590 A074644 A321256 * A319935 A136337 A028601 Adjacent sequences:  A130120 A130121 A130122 * A130124 A130125 A130126 KEYWORD nonn,tabl,easy AUTHOR Gary W. Adamson, May 11 2007 STATUS approved

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Last modified December 5 18:40 EST 2020. Contains 338965 sequences. (Running on oeis4.)