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 A385894 #9 Jul 22 2025 10:33:23 %S A385894 0,1,10,59,228,669,1630,3479,6728,12057,20338,32659,50348,74997, %T A385894 108486,153007,211088,285617,379866,497515,642676,819917,1034286, %U A385894 1291335,1597144,1958345,2382146,2876355,3449404,4110373,4869014,5735775,6721824,7839073,9100202,10518683 %N A385894 a(n) = n^5/5 + n^3/3 + 7*n/15. %D A385894 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Exercise 2.5.17 on page 77. %H A385894 Vincenzo Librandi, <a href="/A385894/b385894.txt">Table of n, a(n) for n = 0..4000</a> %H A385894 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1). %F A385894 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5. %F A385894 G.f.: x*(1 + 4*x + 14*x^2 + 4*x^3 + x^4)/(1 - x)^6. %F A385894 E.g.f.: exp(x)*x*(15 + 60*x + 80*x^2 + 30*x^3 + 3*x^4)/15. %F A385894 a(n) - a(n-1) = A058031(n) for n > 0. %t A385894 a[n_]:=n^5/5+n^3/3+7n/15; Array[a,36,0] %o A385894 (Magma) [n^5/5 + n^3/3 + 7*n/15: n in [0..35]]; // _Vincenzo Librandi_, Jul 22 2025 %Y A385894 Cf. A058031. %K A385894 nonn,easy %O A385894 0,3 %A A385894 _Stefano Spezia_, Jul 12 2025