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A144064
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Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is Euler transform of (j->k).
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26
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1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 3, 0, 1, 4, 9, 10, 5, 0, 1, 5, 14, 22, 20, 7, 0, 1, 6, 20, 40, 51, 36, 11, 0, 1, 7, 27, 65, 105, 108, 65, 15, 0, 1, 8, 35, 98, 190, 252, 221, 110, 22, 0, 1, 9, 44, 140, 315, 506, 574, 429, 185, 30, 0, 1, 10, 54, 192, 490, 918, 1265, 1240, 810, 300, 42, 0
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OFFSET
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0,8
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COMMENTS
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A(n,k) is also the number of partitions of n into parts of k kinds.
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LINKS
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Alois P. Heinz, Antidiagonals n = 0..140, flattened
N. J. A. Sloane, Transforms
Index entries for expansions of Product_{k >= 1} (1-x^k)^m
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FORMULA
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G.f. of column k: Product_{j>=1} 1/(1-x^j)^k.
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 2, 5, 9, 14, 20, ...
0, 3, 10, 22, 40, 65, ...
0, 5, 20, 51, 105, 190, ...
0, 7, 36, 108, 252, 506, ...
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MAPLE
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with (numtheory): etr:= proc(p) local b; b:= proc(n) option remember; `if`(n=0, 1, add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n) end end: A:= (n, k)-> etr(j->k)(n): seq (seq (A(n, d-n), n=0..d), d=0..14);
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CROSSREFS
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Columns 0-24 give: A000007, A000041, A000712, A000716, A023003, A023004, A023005, A023006, A023007, A023008, A023009, A023010, A005758, A023011, A023012, A023013, A023014, A023015, A023016, A023017, A023018, A023019, A023020, A023021, A006922.
Rows 0-2 give: A000012, A001477, A000096.
Diagonal gives: A008485.
Sequence in context: A086460 A136431 A182888 * A172236 A191646 A130020
Adjacent sequences: A144061 A144062 A144063 * A144065 A144066 A144067
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz, Sep 09 2008
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STATUS
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approved
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