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A144048
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Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is Euler transform of (j->j^k).
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0
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1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 6, 5, 1, 1, 9, 14, 13, 7, 1, 1, 17, 36, 40, 24, 11, 1, 1, 33, 98, 136, 101, 48, 15, 1, 1, 65, 276, 490, 477, 266, 86, 22, 1, 1, 129, 794, 1828, 2411, 1703, 649, 160, 30, 1, 1, 257, 2316, 6970, 12729, 11940, 5746, 1593, 282, 42, 1, 1, 513
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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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)^(j^k).
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EXAMPLE
| Square array begins:
1, 1, 1, 1, 1, 1 ...
1, 1, 1, 1, 1, 1 ...
2, 3, 5, 9, 17, 33 ...
3, 6, 14, 36, 98, 276 ...
5, 13, 40, 136, 490, 1828 ...
7, 24, 101, 477, 2411, 12729 ...
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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->j^k)(n); seq (seq (A(n, d-n), n=0..d), d=0..13);
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CROSSREFS
| Columns 0-9 give: A000041, A000219, A023871, A023872, A023873, A023874, A023875, A023876, A023877, A023878. Rows give: 0+1: A000012, 2: A000051, A094373, 3: A001550.
Sequence in context: A154221 A026736 A050446 * A113983 A199333 A089980
Adjacent sequences: A144045 A144046 A144047 * A144049 A144050 A144051
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KEYWORD
| nonn,tabl
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008
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