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 A257890 #30 Mar 15 2024 02:25:47
%S A257890 3,12,34,80,166,314,553,920,1461,2232,3300,4744,6656,9142,12323,16336,
%T A257890 21335,27492,34998,44064,54922,67826,83053,100904,121705,145808,
%U A257890 173592,205464,241860,283246,330119,383008,442475,509116,583562,666480,758574,860586
%N A257890 Expansion of the g.f. (x^2-x+1)*(x^2-3*x+3)/(x-1)^6.
%C A257890 Absolute values of the 5th column of A220074.
%C A257890 Convolution of A000124 and the sequence 3, 6, 10, 15 (the triangular numbers A000217 without the first two entries).
%H A257890 G. C. Greubel, <a href="/A257890/b257890.txt">Table of n, a(n) for n = 0..5000</a>
%H A257890 Kyu-Hwan Lee, Se-jin Oh, <a href="http://arxiv.org/abs/1601.06685">Catalan triangle numbers and binomial coefficients</a>, arXiv:1601.06685 [math.CO], 2016.
%H A257890 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A257890 G.f.: (x^2-x+1)*(x^2-3*x+3)/(x-1)^6.
%F A257890 a(n) = A000292(n+1) + (n+1) + A000389(n+5).
%F A257890 a(n) = (n+1)*(n^4 +14*n^3 +91*n^2 +254*n +360)/120.
%F A257890 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>6. - _Wesley Ivan Hurt_, Jan 27 2016
%F A257890 E.g.f.: (360 + 1080*x + 780*x^2 + 220*x^3 + 25*x^4 + x^5)*exp(x)/120. - _G. C. Greubel_, Nov 24 2017
%t A257890 LinearRecurrence[{6, -15, 20, -15, 6, -1}, {3, 12, 34, 80, 166, 314}, 50] (* _Vincenzo Librandi_, May 12 2015 *)
%o A257890 (Magma) [(n+1)*(n^4+14*n^3+91*n^2+254*n+360)/120: n in [0..40]]; // _Vincenzo Librandi_, May 12 2015
%o A257890 (PARI) Vec((x^2-x+1)*(x^2-3*x+3)/(x-1)^6 + O(x^50)) \\ _Michel Marcus_, Jan 28 2016
%Y A257890 Cf. A000124, A000217, A220074.
%K A257890 nonn,easy
%O A257890 0,1
%A A257890 _R. J. Mathar_, May 12 2015