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 A001557 M4713 N2014 #47 Oct 24 2024 15:29:15
%S A001557 10,55,385,3025,25333,220825,1978405,18080425,167731333,1574304985,
%T A001557 14914341925,142364319625,1367428536133,13202860761145,
%U A001557 128037802953445,1246324856379625,12170706132009733,119179318935377305,1169842891165484965,11506994510201252425
%N A001557 a(n) = 1^n + 2^n + ... + 10^n.
%C A001557 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 A001557 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 A001557 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001557 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001557 T. D. Noe, <a href="/A001557/b001557.txt">Table of n, a(n) for n = 0..200</a>
%H A001557 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 A001557 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=370">Encyclopedia of Combinatorial Structures 370</a>.
%H A001557 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (55, -1320, 18150, -157773, 902055, -3416930, 8409500, -12753576, 10628640, -3628800).
%F A001557 a(n) = Sum_{j=1..10} j^n, n >= 0.
%F A001557 E.g.f.: exp(x) + exp(2*x) + exp(3*x) + exp(4*x) + exp(5*x) + exp(6*x) + exp(7*x) + exp(8*x) + exp(9*x) + exp(10*x). - _Vladeta Jovovic_, May 08 2002
%F A001557 From _Wolfdieter Lang_, Oct 15 2011: (Start)
%F A001557 O.g.f.: (2 - 11*x) *(5 - 220*x + 4070*x^2 - 41140*x^3 + 247049*x^4 - 896368*x^5 + 1903836*x^6 - 2143152*x^7 + 966240*x^8)/Product_{j=1..10} (1 - j*x).
%F A001557 From the e.g.f. via Laplace transformation. See the proof in a link under A196837.
%F A001557 (End)
%F A001557 a(n) = A001556(n) + A011557(n). - _Michel Marcus_, Jul 26 2013
%t A001557 Table[Total[Range[10]^n], {n, 0, 20}] (* _T. D. Noe_, Aug 09 2012 *)
%o A001557 (Python)
%o A001557 def A001557(n): return sum(i**n for i in range(1,11)) # _Chai Wah Wu_, Oct 24 2024
%Y A001557 Column 10 of array A103438. Cf. A196837.
%K A001557 nonn,easy
%O A001557 0,1
%A A001557 _N. J. A. Sloane_
%E A001557 More terms from _Jon E. Schoenfield_, Mar 24 2010