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A144042
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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 Euler transform applied k times.
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8
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1, 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 8, 9, 1, 1, 5, 13, 25, 20, 1, 1, 6, 19, 51, 77, 48, 1, 1, 7, 26, 89, 197, 258, 115, 1, 1, 8, 34, 141, 410, 828, 871, 286, 1, 1, 9, 43, 209, 751, 2052, 3526, 3049, 719, 1, 1, 10, 53, 295, 1260, 4337, 10440, 15538, 10834, 1842, 1, 1, 11, 64
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..1035
N. J. A. Sloane, Transforms
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EXAMPLE
| Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
2, 3, 4, 5, 6, 7, ...
4, 8, 13, 19, 26, 34, ...
9, 25, 51, 89, 141, 209, ...
20, 77, 197, 410, 751, 1260, ...
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MAPLE
| with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: A:= proc(n, k) local a, b, t; b[1]:= etr(a); for t from 2 to k do b[t]:= etr(b[t-1]) 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..15);
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CROSSREFS
| Columns 1-9 give: A000081, A007563, A144035, A144036, A144037, A144038, A144039, A144040, A144041. Rows 2-4 give: A000012, A000027, A034856.
Sequence in context: A092422 A096465 A124460 * A122084 A104559 A080853
Adjacent sequences: A144039 A144040 A144041 * A144043 A144044 A144045
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KEYWORD
| eigen,nonn,tabl
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008
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