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 A051128 Table T(n,k) = n^k read by antidiagonals (n >= 1, k >= 1). 8
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sum of anti-diagonals is A003101(n) for n>0. - Alford Arnold, Jan 14 2007 LINKS 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 FORMULA 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 EXAMPLE Table begins 1 1 1 1 1 ... 2 4 8 16 32 ... 3 9 27 81 243 ... 4 16 64 256 1024 ... MAPLE 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 MATHEMATICA Table[n^(k - n + 1), {k, 1, 11}, {n, k, 1, -1}] // Flatten (* Jean-François Alcover, Dec 14 2012 *) CROSSREFS 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 KEYWORD nonn,tabl,easy,nice AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 11 1999 STATUS approved

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