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Search: id:A144823
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| A144823 |
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Square array A(n,k), n>=1, k>=1, read by antidiagonals, with A(1,k)=1 and sequence a_k of column k shifts left when Dirichlet convolution with a_k (DC:(b,a_k)->a) applied k times. |
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1
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| 1, 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 9, 9, 1, 1, 5, 16, 30, 18, 1, 1, 6, 25, 70, 90, 40, 1, 1, 7, 36, 135, 280, 288, 80, 1, 1, 8, 49, 231, 675, 1168, 864, 168, 1, 1, 9, 64, 364, 1386, 3475, 4672, 2647, 340, 1, 1, 10, 81, 540, 2548, 8496, 17375, 18884, 7968, 698, 1, 1, 11, 100
(list; table; graph; listen)
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OFFSET
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1,6
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LINKS
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N. J. A. Sloane, Transforms
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EXAMPLE
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Square array begins:
1 1 1 1 1 ...
1 1 1 1 1 ...
2 3 4 5 6 ...
4 9 16 25 36 ...
9 30 70 135 231 ...
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MAPLE
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with (numtheory): dc:= proc(b, c) proc(n) option remember; add (b(d) *c(n/d), d=`if`(n<0, {}, divisors(n))) end end: A:= proc(n, k) local a, b, t; b[1]:= dc(a, a); for t from 2 to k do b[t]:= dc(b[t-1], a) od: a:= n-> `if`(n=1, 1, b[k](n-1)); a(n) end: seq (seq (A(n, d-n), n=1..d-1), d=2..13);
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CROSSREFS
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Rows 1+2, 3-4 give: A000012, A000027, A000290, A002414. Columns 1-9 give: A038044, A144817, A144316, A144818, A144819, A144820, A144317, A144821, A144822.
Sequence in context: A071922 A138028 A009999 this_sequence A098446 A098447 A162717
Adjacent sequences: A144820 A144821 A144822 this_sequence A144824 A144825 A144826
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KEYWORD
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eigen,nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 21 2008
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