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A001923 a(n) = Sum_{k=1..n} k^k.
(Formerly M3968 N1639)
22
0, 1, 5, 32, 288, 3413, 50069, 873612, 17650828, 405071317, 10405071317, 295716741928, 9211817190184, 312086923782437, 11424093749340453, 449317984130199828, 18896062057839751444, 846136323944176515621 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 R. Povolotsky, Sep 01 2007

From Luan Alberto Ferreira, Aug 01 2017: (Start)

If n == 0 or 3 (mod 4), then a(n) == 0 (mod 4).

If n == 0, 4, 7, 14, 15 or 17 (mod 18), then a(n) == 0 (mod 3). (End)

REFERENCES

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 308.

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

T. D. Noe, Table of n, a(n) for n=0..100

Mohammad K. Azarian, On the hyperfactorial function, hypertriangular function and the discriminants of certain polynomials. Int. J. Pure Appl. Math. 36 (2007), 251-257.

G. W. Wishard & F. Underwood, Problem 4155, Amer. Math. Monthly, 53 (1946), 471.

FORMULA

a(n+1)/a(n) > e*n and a(n+1)/a(n) is asymptotic to e*n. - Benoit Cloitre, Sep 29 2002

For n > 0: a(n) = a(n-1) + A000312(n). - Reinhard Zumkeller, Jul 11 2014

MATHEMATICA

Accumulate[Join[{0}, Table[k^k, {k, 20}]]] (* Harvey P. Dale, Feb 11 2015 *)

PROG

(PARI) for(n=1, 20, print1(sum(x=1, n, x^x), ", ")) \\ Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 24 2004

(Haskell)

a001923 n = a001923_list !! n

a001923_list = scanl (+) 0 $ tail a000312_list

-- Reinhard Zumkeller, Jul 11 2014

CROSSREFS

Cf. A073825, A062970 (another version).

Cf. A062815, A060946, A117887.

Cf. A000312.

Sequence in context: A068102 A166993 A265130 * A257710 A023880 A104031

Adjacent sequences:  A001920 A001921 A001922 * A001924 A001925 A001926

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 25 22:27 EST 2018. Contains 299662 sequences. (Running on oeis4.)