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A001554
a(n) = 1^n + 2^n + ... + 7^n.
(Formerly M4393 N1850)
6
7, 28, 140, 784, 4676, 29008, 184820, 1200304, 7907396, 52666768, 353815700, 2393325424, 16279522916, 111239118928, 762963987380, 5249352196144, 36210966447236, 250337422025488, 1733857359003860, 12027604452404464, 83544895168776356, 580964060390826448
OFFSET
0,1
COMMENTS
Conjectures for o.g.f.s for this type of sequences appear in the PhD thesis by Simon Plouffe. See A001552 for the reference. These conjectures are proved in a link given in A196837. - Wolfdieter Lang, Oct 15 2011
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 813.
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
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Index entries for linear recurrences with constant coefficients, signature (28, -322, 1960, -6769, 13132, -13068, 5040).
FORMULA
From Wolfdieter Lang, Oct 15 2011: (Start)
E.g.f.: (1-exp(7*x))/(exp(-x)-1) = Sum_{j=1..7} exp(j*x) (trivial).
O.g.f.: (7 - 168*x + 1610*x^2 - 7840*x^3 + 20307*x^4 - 26264*x^5 + 13068*x^6)/Product_{j=1..7} (1 - j*x). From the e.g.f. via Laplace transformation. See the proof in a link under A196837. (End)
MAPLE
A001554:=n->add(i^n, i=1..7): seq(A001554(n), n=0..30); # Wesley Ivan Hurt, Jul 15 2014
MATHEMATICA
Table[Total[Range[7]^n], {n, 0, 20}]
PROG
(Magma) [1+2^n+3^n+4^n+5^n+6^n+7^n : n in [0..30]]; // Wesley Ivan Hurt, Jul 15 2014
CROSSREFS
Column 7 of array A103438. A196837.
Sequence in context: A238448 A290356 A025030 * A370243 A370103 A359723
KEYWORD
nonn,easy,changed
EXTENSIONS
More terms from Jon E. Schoenfield, Mar 24 2010
STATUS
approved