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%I M4149 N1723 #51 Feb 02 2022 04:06:43
%S 6,21,91,441,2275,12201,67171,376761,2142595,12313161,71340451,
%T 415998681,2438235715,14350108521,84740914531,501790686201,
%U 2978035877635,17706908038281,105443761093411,628709267031321,3752628871164355,22418196307542441,134023513204581091
%N a(n) = 1^n + 2^n + ... + 6^n.
%C For the o.g.f.s of such sequences see the W. Lang link under A196837. The e.g.f.s are trivial. - _Wolfdieter Lang_, Oct 14 2011
%C a(n) is divisible by 7 iff n is not divisible by 6 (see De Koninck & Mercier reference). Example: a(5)= 12201 = 7 * 1743 and a(6) = 67171 = 9595 * 7 + 6. - _Bernard Schott_, Mar 06 2020
%D 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 J.-M. De Koninck and A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 289 pp. 45, 194, Ellipses, Paris, (2004).
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001553/b001553.txt">Table of n, a(n) for n = 0..200</a>
%H 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 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=366">Encyclopedia of Combinatorial Structures 366</a>
%F a(n) = Sum_{k=1..6} k^n.
%F From _Wolfdieter Lang_, Oct 10 2011: (Start)
%F E.g.f.: (1-exp(6*x))/(exp(-x)-1) = Sum_{j=1..6} exp(j*x) (trivial).
%F O.g.f.: (2 - 7*x)*(3 - 42*x + 203*x^2 - 392*x^3 + 252*x^4)/Product_{j=1..6} (1 - j*x).
%F From the Laplace transformation of the e.g.f. (with argument 1/p, and multiplied with 1/p), which yields the partial fraction decomposition of the given o.g.f., namely Sum_{j=1..6} 1/(1 - j*x).
%F (End)
%t Table[Total[Range[6]^n], {n, 0, 40}] (* _T. D. Noe_, Oct 10 2011 *)
%Y Column 6 of array A103438, A001552.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Jon E. Schoenfield_, Mar 24 2010
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