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A051128
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Table T(n,k) = n^k read by antidiagonals (n >= 1, k >= 1).
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8
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1, 2, 1, 3, 4, 1, 4, 9, 8, 1, 5, 16, 27, 16, 1, 6, 25, 64, 81, 32, 1, 7, 36, 125, 256, 243, 64, 1, 8, 49, 216, 625, 1024, 729, 128, 1, 9, 64, 343, 1296, 3125, 4096, 2187, 256, 1, 10, 81, 512, 2401, 7776, 15625, 16384, 6561, 512, 1, 11, 100, 729, 4096, 16807, 46656
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table;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Sum of anti-diagonals is A003101(n) for n>0. - Alford Arnold, Jan 14 2007
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LINKS
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T. D. Noe, Rows n=1..50 of triangle, flattened
G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees
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FORMULA
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a(n) = A004736(n)^A002260(n) or ((t*t+3*t+4)/2-n)^(n-(t*(t+1)/2)), where t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 14 2012
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EXAMPLE
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Table begins
1 1 1 1 1 ...
2 4 8 16 32 ...
3 9 27 81 243 ...
4 16 64 256 1024 ...
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MAPLE
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A051128 := proc(n) # Boris Putievskiy's formula
a := floor((sqrt(8*n-7)+1)/2);
b := (a+a^2)/2-n;
c := (a-a^2)/2+n;
(b+1)^c end:
seq(A051128(n), n=1..61); # Peter Luschny, Dec 14 2012
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MATHEMATICA
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Table[n^(k - n + 1), {k, 1, 11}, {n, k, 1, -1}] // Flatten (* Jean-François Alcover, Dec 14 2012 *)
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CROSSREFS
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Cf. A051129, A003992, A004248, A033918, A095891, A220415, A220416, A220417.
Cf. A003101.
Sequence in context: A171275 A107616 A055208 * A137614 A204213 A143326
Adjacent sequences: A051125 A051126 A051127 * A051129 A051130 A051131
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from James A. Sellers, Dec 11 1999
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STATUS
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approved
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