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 A332698 #9 Sep 13 2024 18:04:23
%S A332698 0,6,25,65,134,240,391,595,860,1194,1605,2101,2690,3380,4179,5095,
%T A332698 6136,7310,8625,10089,11710,13496,15455,17595,19924,22450,25181,28125,
%U A332698 31290,34684,38315,42191,46320,50710,55369,60305,65526,71040,76855,82979,89420,96186
%N A332698 a(n) = (8*n^3 + 15*n^2 + 13*n)/6.
%C A332698 The end values of the partial rows on the main diagonal of A332662 in the representation in the example section.
%H A332698 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F A332698 a(n) = [x^n] (x*(x^2 + x + 6))/(x - 1)^4.
%F A332698 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A332698 a(n) = binomial(n+2, 3) + binomial(n+1, 3) + 2*(n+1)*binomial(n+1, 2) + binomial(n, 1) = A331987(n) + n.
%p A332698 a := n -> (8*n^3 + 15*n^2 + 13*n)/6: seq(a(n), n=0..41);
%p A332698 gf := (x*(x^2 + x + 6))/(x - 1)^4: ser := series(gf, x, 44):
%p A332698 seq(coeff(ser, x, n), n=0..41);
%t A332698 LinearRecurrence[{4, -6, 4, -1}, {0, 6, 25, 65}, 42]
%t A332698 Table[(8n^3+15n^2+13n)/6,{n,0,50}] (* _Harvey P. Dale_, Sep 13 2024 *)
%Y A332698 Cf. A332662, A331987.
%K A332698 nonn,easy
%O A332698 0,2
%A A332698 _Peter Luschny_, Feb 20 2020