

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
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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/(12*x*y).  R. J. Mathar, Aug 11 2015


EXAMPLE

First few terms of the triangle are:
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 (* JeanFrançois 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



