|
Search: id:A001923
|
|
|
| A001923 |
|
Sum k^k, k=1..n.
(Formerly M3968 N1639)
|
|
+0
15
|
|
| 0, 1, 5, 32, 288, 3413, 50069, 873612, 17650828, 405071317, 10405071317, 295716741928, 9211817190184, 312086923782437, 11424093749340453, 449317984130199828, 18896062057839751444, 846136323944176515621
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..100
|
|
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
|
|
MATHEMATICA
|
lst={}; s=0; Do[AppendTo[lst, s+=n^n], {n, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
|
|
PROGRAM
|
(PARI) for(a=1, 20, print((sum(x=1, a, x^x)))) - Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 24 2004
|
|
CROSSREFS
|
Cf. A073825, A062970 (another version).
Cf. A062815, A060946, A117887.
Adjacent sequences: A001920 A001921 A001922 this_sequence A001924 A001925 A001926
Sequence in context: A102231 A127089 A068102 this_sequence A023880 A104031 A023882
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
