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 A002489 a(n) = n^(n^2), or (n^n)^n. (Formerly M5030 N2170) 45
 1, 1, 16, 19683, 4294967296, 298023223876953125, 10314424798490535546171949056, 256923577521058878088611477224235621321607, 6277101735386680763835789423207666416102355444464034512896, 196627050475552913618075908526912116283103450944214766927315415537966391196809 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The number of closed binary operations on a set of order n. Labeled groupoids. The values of "googol" in base N: "10^100" in base 2 is 2^4=16; "10^100" in base 3 is 3^9=19683, etc. This is N^^3 by the "lower-valued" (left-associative) definition of the hyper4 or tetration operator (see Munafo webpage). - Robert Munafo, Jan 25 2010 n^(n^k) = (((n^n)^n)^...)^n, with k+1 n's, k >= 0. - Daniel Forgues, May 18 2013 REFERENCES J. S. Rose, A Course on Group Theory, Camb. Univ. Press, 1978, see p. 6. P. Rossier, Grands nombres, Elemente der Mathematik, 3 (1948), 20. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi and Michael Lee, Table of n, a(n) for n = 0..26 (Vincenzo Librandi supplied the first 16 terms) R. Munafo, Hyper4 Iterated Exponential Function [From Robert Munafo, Jan 25 2010] Eric Postpischil Posting to sci.math newsgroup, May 21 1990 FORMULA a(n) = [x^(n^2)] 1/(1 - n*x). - Ilya Gutkovskiy, Oct 10 2017 EXAMPLE a(3) = 19683 because (3^3)^3 = 3^(3^2) = 19683. MATHEMATICA Join[{1}, Table[n^n^2, {n, 10}]] (* Harvey P. Dale, Sep 06 2011 *) PROG (MAGMA) [n^(n^2): n in [0..10]]; // Vincenzo Librandi, May 13 2011 (PARI) a(n)=n^(n^2) \\ Charles R Greathouse IV, Nov 20 2012 CROSSREFS a(n) = A079172(n) + A023814(n) = A079176(n) + A079179(n); a(n) = A079182(n) + A023813(n) = A079186(n) + A079189(n); a(n) = A079192(n) + A079195(n) + A079198(n) + A023815(n). Cf. A002488, A001329, A002488, A023813, A076113, A090588, A000312. Sequence in context: A098175 A089232 A300615 * A060205 A140597 A017296 Adjacent sequences:  A002486 A002487 A002488 * A002490 A002491 A002492 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified March 18 13:47 EDT 2019. Contains 321289 sequences. (Running on oeis4.)