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 A047661 #20 Sep 02 2025 09:48:02
%S A047661 5,30,115,340,841,1826,3591,6536,11181,18182,28347,42652,62257,88522,
%T A047661 123023,167568,224213,295278,383363,491364,622489,780274,968599,
%U A047661 1191704,1454205,1761110,2117835,2530220,3004545,3547546,4166431,4868896,5663141,6557886,7562387
%N A047661 Row 5 of square array defined in A047662.
%H A047661 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A047661 a(n) = (n/15)*(2*n^4 + 5*n^3 + 20*n^2 + 25*n + 23). [Corrected by _Sean A. Irvine_, May 13 2021]
%F A047661 From _Elmo R. Oliveira_, Sep 02 2025: (Start)
%F A047661 G.f.: x*(5 + 10*x^2 + x^4)/(x-1)^6.
%F A047661 E.g.f.: x*(5 + 5*x + x^2)*(15 + 15*x + 2*x^2)*exp(x)/15.
%F A047661 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. (End)
%t A047661 Table[(n/15)(2n^4+5n^3+20n^2+25n+23),{n,30}] (* _Harvey P. Dale_, Nov 25 2022 *)
%o A047661 (PARI) my(x='x+O('x^35)); Vec(x*(5+10*x^2+x^4)/(1-x)^6) \\ _Elmo R. Oliveira_, Sep 02 2025
%Y A047661 Cf. A047662.
%K A047661 nonn,easy,changed
%O A047661 1,1
%A A047661 _N. J. A. Sloane_
%E A047661 More terms from _Elmo R. Oliveira_, Sep 02 2025