|
Search: id:A023037
|
|
|
| A023037 |
|
(n^n-1)/(n-1) = n^0+n^1+...+n^(n-1). |
|
+0
15
|
|
| 0, 1, 3, 13, 85, 781, 9331, 137257, 2396745, 48427561, 1111111111, 28531167061, 810554586205, 25239592216021, 854769755812155, 31278135027204241, 1229782938247303441, 51702516367896047761, 2314494592664502210319
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
For prime n, a(n) is conjectured to be the period of Bell numbers (mod n). See A054767. - T. D. Noe, Oct 12 2007
|
|
REFERENCES
|
W. F. Lunnon et al., Arithmetic properties of Bell numbers to a composite modulus I, Acta Arith., 35 (1979), 1-16. [From N. J. A. Sloane (njas(AT)research.att.com), Feb 07 2009]
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..100
|
|
FORMULA
|
Also sum (n^(n-j),j=1..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 11 2006
a(n) = A125118(n,n-1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 21 2006
|
|
EXAMPLE
|
a(3) = 3^0 + 3^1 + 3^2 = 1+3+9 = 13.
|
|
MATHEMATICA
|
lst={}; Do[s=0; Do[s+=n^a, {a, 0, n-1}]; AppendTo[lst, s], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 27 2009]
|
|
PROGRAM
|
(Other) sage: [lucas_number1(n, n+1, n) for n in xrange(0, 19)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]
|
|
CROSSREFS
|
Cf. A088790 (n such that a(n) is prime). Cf. A001039.
Sequence in context: A152789 A125500 A121679 this_sequence A157451 A152112 A054420
Adjacent sequences: A023034 A023035 A023036 this_sequence A023038 A023039 A023040
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
David W. Wilson (davidwwilson(AT)comcast.net)
|
|
EXTENSIONS
|
Entry improved by Tobias Nipkow (nipkow(AT)in.tum.de).
|
|
|
Search completed in 0.005 seconds
|
