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A128229
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A natural number transform, inverse of signed A094587.
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17
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1, 1, 1, 0, 2, 1, 0, 0, 3, 1, 0, 0, 0, 4, 1, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 7, 1, 0, 0, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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Signed version of the transform (with -1, -2, -3, ... in the subdiagonal) gives A094587 having row sums A000522: (1, 2, 5, 16, 65, 236, ...). Unsigned inverse gives signed A094587 (with alternate signs); giving row sums = a signed variation of A094587 as follows: (1, 0, 1, -2, 9, -44, 265, -1854, ...). Binomial transform of the triangle = A093375.
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LINKS
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FORMULA
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Infinite lower triangular matrix with (1,1,1,...) in the main diagonal and (1,2,3,...) in the subdiagonal.
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
0, 2, 1;
0, 0, 3, 1;
0, 0, 0, 4, 1;
0, 0, 0, 0, 5, 1;
0, 0, 0, 0, 0, 6, 1;
0, 0, 0, 0, 0, 0, 7, 1;
...
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MATHEMATICA
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a128229[n_] := Table[Which[r==q, 1, r-1==q, q, True, 0], {r, 1, n}, {q, 1, r}]
Flatten[a128229[13]] (* data *)
TableForm[a128229[8]] (* triangle *)
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PROG
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(Python)
def T(n, k): return 1 if n==k else n - 1 if k==n - 1 else 0
for n in range(1, 11): print([T(n, k) for k in range(1, n + 1)]) # Indranil Ghosh, Jun 10 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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