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A144074
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Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is Euler transform of the powers of k.
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7
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1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 7, 3, 0, 1, 4, 15, 20, 5, 0, 1, 5, 26, 64, 59, 7, 0, 1, 6, 40, 148, 276, 162, 11, 0, 1, 7, 57, 285, 843, 1137, 449, 15, 0, 1, 8, 77, 488, 2020, 4632, 4648, 1200, 22, 0, 1, 9, 100, 770, 4140, 13876, 25124, 18585, 3194, 30, 0, 1, 10, 126
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| G.f. of column k: Product_{j>=1} 1/(1-x^j)^(k^j).
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EXAMPLE
| Square array begins:
1, 1, 1, 1, 1, 1 ...
0, 1, 2, 3, 4, 5 ...
0, 2, 7, 15, 26, 40 ...
0, 3, 20, 64, 148, 285 ...
0, 5, 59, 276, 843, 2020 ...
0, 7, 162, 1137, 4632, 13876 ...
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MAPLE
| 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^j)(n); seq (seq (A(n, d-n), n=0..d), d=0..14);
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CROSSREFS
| Columns 0-9 give: A000007, A000041, A034899, A144067, A144068, A144069, A144070, A144071, A144072, A144073. Rows 0-2 give: A000012, A001477, A005449.
Sequence in context: A091063 A198793 A085388 * A124540 A124550 A146326
Adjacent sequences: A144071 A144072 A144073 * A144075 A144076 A144077
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KEYWORD
| nonn,tabl
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 09 2008
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