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 A001556 M4627 N1977 #35 Oct 26 2024 10:18:46
%S A001556 9,45,285,2025,15333,120825,978405,8080425,67731333,574304985,
%T A001556 4914341925,42364319625,367428536133,3202860761145,28037802953445,
%U A001556 246324856379625,2170706132009733,19179318935377305,169842891165484965,1506994510201252425
%N A001556 a(n) = 1^n + 2^n + ... + 9^n.
%C A001556 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 the link given in A196837. - _Wolfdieter Lang_, Oct 15 2011
%D A001556 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 A001556 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001556 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001556 T. D. Noe, <a href="/A001556/b001556.txt">Table of n, a(n) for n = 0..200</a>
%H A001556 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 A001556 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=369">Encyclopedia of Combinatorial Structures 369</a>
%H A001556 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (45, -870, 9450, -63273, 269325, -723680, 1172700, -1026576, 362880).
%F A001556 a(n) = sum_{j=1..9} j^n, n>=0.
%F A001556 From _Wolfdieter Lang_, Oct 15 2011: (Start)
%F A001556 E.g.f.: (1-exp(9*x))/(exp(-x)-1) = sum(exp(j*x),j=1..9) (trivial).
%F A001556 O.g.f.: (9 - 360*x + 6090*x^2 - 56700*x^3 + 316365*x^4 - 1077300*x^5 + 2171040*x^6 - 2345400*x^7 + 1026576*x^8)/product_{j=1..9} (1-j*x).
%F A001556 From the e.g.f. via Laplace transformation. See the proof in a link under A196837.
%F A001556 (End)
%F A001556 a(n) = A001555(n) + A001019(n). - _Michel Marcus_, Jul 26 2013
%t A001556 Table[Total[Range[9]^n], {n, 0, 20}] (* _T. D. Noe_, Aug 09 2012 *)
%Y A001556 Column 9 of array A103438. A196837.
%K A001556 nonn
%O A001556 0,1
%A A001556 _N. J. A. Sloane_
%E A001556 More terms from _Jon E. Schoenfield_, Mar 24 2010