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 A304725 #26 Jan 23 2025 19:46:16
%S A304725 2,47,194,527,1154,2207,3842,6239,9602,14159,20162,27887,37634,49727,
%T A304725 64514,82367,103682,128879,158402,192719,232322,277727,329474,388127,
%U A304725 454274,528527,611522,703919,806402,919679,1044482,1181567,1331714,1495727,1674434,1868687
%N A304725 a(n) = n^4 + 8*n^3 + 20*n^2 + 16*n + 2.
%H A304725 Rigoberto Florez, Robinson A. Higuita and Antara Mukherjee, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Mukherjee/mukh2.html">Alternating Sums in the Hosoya Polynomial Triangle</a>, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.5 (see formula for B_4(x) on page 4).
%H A304725 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A304725 G.f.: (2 + 37*x - 21*x^2 + 7*x^3 - x^4)/(1 - x)^5.
%F A304725 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A304725 a(n) = A008865(n+2)^2 - 2. Therefore, a(n) is a member of A008865.
%t A304725 Table[n^4 + 8 n^3 + 20 n^2 + 16 n + 2, {n, 0, 40}]
%t A304725 LinearRecurrence[{5,-10,10,-5,1},{2,47,194,527,1154},50] (* _Harvey P. Dale_, Jan 23 2025 *)
%o A304725 (Magma) [n^4+8*n^3+20*n^2+16*n+2: n in [0..40]];
%Y A304725 Cf. A008865.
%Y A304725 Fourth column of the array in A298675 (without -1).
%Y A304725 Fifth column of the array in A299741.
%K A304725 nonn,easy
%O A304725 0,1
%A A304725 _Vincenzo Librandi_, May 30 2018