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A001923
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Sum k^k, k=1..n.
(Formerly M3968 N1639)
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19
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0, 1, 5, 32, 288, 3413, 50069, 873612, 17650828, 405071317, 10405071317, 295716741928, 9211817190184, 312086923782437, 11424093749340453, 449317984130199828, 18896062057839751444, 846136323944176515621
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = A062970(n) - 1.
Starting from the second term, 1, the terms could be described as the special case (n=1; j=1) of the following general formula: a(n) = <from k=j to k=i> Sum [(n + k - 1)]^(k) n=1; j=1; i=1,2,3,...,... For (n=0; j=1) the formula yields A062815 n=0; j=1; i=2,3,4,... For (n=2; j=0) we get A060946 and for (n=3; j=0) A117887. - Alexander Povolotsky (pevnev(AT)juno.com), Sep 01 2007
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REFERENCES
| Azarian, Mohammad K., On the hyperfactorial function, hypertriangular function and the discriminants of certain polynomials. Int. J. Pure Appl. Math. 36 (2007), 251-257.
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 308.
Problem 4155, Amer. Math. Monthly, 53 (1946), 471.
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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
| a(n+1)/a(n) > e*n and a(n+1)/a(n) is asymptotic to e*n - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 29 2002
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MATHEMATICA
| lst={}; s=0; Do[AppendTo[lst, s+=n^n], {n, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
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PROG
| (PARI) for(a=1, 20, print((sum(x=1, a, x^x)))) - Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 24 2004
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CROSSREFS
| Cf. A073825, A062970 (another version).
Cf. A062815, A060946, A117887.
Sequence in context: A198598 A068102 A166993 * A023880 A104031 A023882
Adjacent sequences: A001920 A001921 A001922 * A001924 A001925 A001926
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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