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 A290312 #16 Sep 01 2018 17:38:12 %S A290312 1,8,29,75,160,301,518,834,1275,1870,2651,3653,4914,6475,8380,10676, %T A290312 13413,16644,20425,24815,29876,35673,42274,49750,58175,67626,78183, %U A290312 89929,102950,117335,133176,150568,169609,190400,213045,237651,264328,293189,324350,357930 %N A290312 Third diagonal sequence of the Sheffer triangle A094816 (special Charlier). %C A290312 See A094816 and A290311. %H A290312 Colin Barker, <a href="/A290312/b290312.txt">Table of n, a(n) for n = 0..1000</a> %H A290312 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1). %F A290312 G.f.: (1 + 3*x - x^2)/(1 - x)^5. %F A290312 E.g.f.: exp(x)*(1 + 7*x + 14*x^2/2! + 11*x^3/3! + 3*x^4/4!). This is computed from the o.g.f. with eqs. (23)-(25) of the _Wolfdieter Lang_ 2017 link in A282629. %F A290312 From _Colin Barker_, Jul 29 2017: (Start) %F A290312 a(n) = (24 + 70*n + 69*n^2 + 26*n^3 + 3*n^4) / 24. %F A290312 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4. %F A290312 (End) %o A290312 (PARI) Vec((1 + 3*x - x^2)/(1 - x)^5 + O(x^60)) \\ _Colin Barker_, Jul 29 2017 %Y A290312 Cf. A094816, A290311. %K A290312 nonn,easy %O A290312 0,2 %A A290312 _Wolfdieter Lang_, Jul 28 2017