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 A101097 #37 Jan 14 2025 10:39:29
%S A101097 1,12,69,272,846,2232,5214,11088,21879,40612,71643,121056,197132,
%T A101097 310896,476748,713184,1043613,1497276,2110273,2926704,3999930,5393960,
%U A101097 7184970,9462960,12333555,15919956,20365047,25833664,32515032,40625376,50410712
%N A101097 a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(2 + 4*n + n^2)/840.
%C A101097 Fourth partial sums of cubes (A000578). Partial sums of A101094.
%H A101097 G. C. Greubel, <a href="/A101097/b101097.txt">Table of n, a(n) for n = 1..5000</a>
%H A101097 Feihu Liu, Guoce Xin, and Chen Zhang, <a href="https://arxiv.org/abs/2412.18744">Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS</a>, arXiv:2412.18744 [math.CO], 2024. See p. 15.
%H A101097 C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a>. [broken link]
%H A101097 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A101097 a(n) = n*(n+1)*(n+2)*(n+3)*...*(n+k)*(n*(n+k) + (k-1)*k/6)/((k+3)!/6) for k=4. - _Alexander R. Povolotsky_, May 17 2008
%F A101097 G.f.: x*(1 + 4*x + x^2)/(1-x)^8. - _R. J. Mathar_, Jun 13 2008
%F A101097 a(n) = Sum_{k=1..n} A000217(k)^2*A000217(n-k+1). - _Bruno Berselli_, Sep 04 2013
%F A101097 E.g.f.: x*(840 + 4200*x + 5040*x^2 + 2240*x^3 + 427*x^4 + 35*x^5 + x^6) *exp(x)/840. - _G. C. Greubel_, Dec 01 2018
%t A101097 Table[Binomial[n+4,5]*(2+4*n+n^2)/7, {n,0,50}] (* _G. C. Greubel_, Feb 17 2017 *)
%o A101097 (PARI) {A101097(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(2+4*n+n^2)/840} \\ _R. J. Mathar_, Dec 06 2011
%o A101097 (Magma) A000217:=func<i | i*(i+1)/2>; [&+[A000217(k)^2*A000217(n-k+1): k in [1..n]]: n in [1..40]]; // _Bruno Berselli_, Sep 04 2013
%o A101097 (Sage) [binomial(n+4,5)*(2+4*n+n^2)/7 for n in (1..40)] # _G. C. Greubel_, Dec 01 2018
%Y A101097 Cf. A000217, A101102, A101094, A024166, A000537.
%K A101097 nonn,easy
%O A101097 1,2
%A A101097 Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
%E A101097 Edited by _Ralf Stephan_, Dec 16 2004