This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A001554 M4393 N1850 #46 Oct 26 2024 10:16:03
%S A001554 7,28,140,784,4676,29008,184820,1200304,7907396,52666768,353815700,
%T A001554 2393325424,16279522916,111239118928,762963987380,5249352196144,
%U A001554 36210966447236,250337422025488,1733857359003860,12027604452404464,83544895168776356,580964060390826448
%N A001554 a(n) = 1^n + 2^n + ... + 7^n.
%C A001554 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
%D A001554 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.
%D A001554 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001554 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001554 T. D. Noe, <a href="/A001554/b001554.txt">Table of n, a(n) for n = 0..200</a>
%H A001554 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A001554 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=367">Encyclopedia of Combinatorial Structures 367</a>
%H A001554 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A001554 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (28, -322, 1960, -6769, 13132, -13068, 5040).
%F A001554 From _Wolfdieter Lang_, Oct 15 2011: (Start)
%F A001554 E.g.f.: (1-exp(7*x))/(exp(-x)-1) = Sum_{j=1..7} exp(j*x) (trivial).
%F A001554 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)
%p A001554 A001554:=n->add(i^n, i=1..7): seq(A001554(n), n=0..30); # _Wesley Ivan Hurt_, Jul 15 2014
%t A001554 Table[Total[Range[7]^n], {n, 0, 20}]
%o A001554 (Magma) [1+2^n+3^n+4^n+5^n+6^n+7^n : n in [0..30]]; // _Wesley Ivan Hurt_, Jul 15 2014
%Y A001554 Column 7 of array A103438. A196837.
%K A001554 nonn,easy
%O A001554 0,1
%A A001554 _N. J. A. Sloane_
%E A001554 More terms from _Jon E. Schoenfield_, Mar 24 2010