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 A259563 #16 Sep 02 2024 12:00:32
%S A259563 0,0,2571912,2472394752,138662798400,1666179072000,-4637478825000,
%T A259563 -272992368918528,-3187483870330368,-23209723979366400,
%U A259563 -126970182577359000,-566493158246400000,-2161675076294530368,-7278963158259007488,-22112928086617859400,-61611251010011136000
%N A259563 a(n) = 81*n^3*(n-1)^5*(n+1)^2*(n^2-6*n+1)*(n^3-79*n^2+163*n-81).
%H A259563 M. P. Delest, <a href="http://dx.doi.org/10.1016/0097-3165(88)90071-4">Generating functions for column-convex polyominoes</a>, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31. See expression F in Theorem 16 page 29.
%H A259563 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
%F A259563 G.f.: 52488*x^2*(49 + 46320*x + 1894016*x^2 - 4899760*x^3 - 305530185*x^4 - 1372006208*x^5 - 1287460720*x^6 + 1418574528*x^7 + 2422309735*x^8 + 1000206160*x^9 + 139190784*x^10 + 5654000*x^11 + 37281*x^12)/(1-x)^16.
%F A259563 a(n) = 16*a(n-1) - 120*a(n-2) + 560*a(n-3) - 1820*a(n-4) + 4368*a(n-5) - 8008*a(n-6) + 11440*a(n-7) - 12870*a(n-8) + 11440*a(n-9) - 8008*a(n-10) + 4368*a(n-11) - 1820*a(n-12) + 560*a(n-13) - 120*a(n-14) + 16*a(n-15) - a(n-16).
%t A259563 Table[81 n^3 (n-1)^5 (n+1)^2 (n^2 - 6 n + 1) (n^3 - 79 n^2 + 163 n - 81), {n, 0, 23}]
%t A259563 LinearRecurrence[{16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1},{0,0,2571912,2472394752,138662798400,1666179072000,-4637478825000,-272992368918528,-3187483870330368,-23209723979366400,-126970182577359000,-566493158246400000,-2161675076294530368,-7278963158259007488,-22112928086617859400,-61611251010011136000},20] (* _Harvey P. Dale_, Sep 02 2024 *)
%o A259563 (Magma) [81*n^3*(n-1)^5*(n+1)^2*(n^2-6*n+1)*(n^3-79*n^2+163*n-81): n in [0..20]];
%Y A259563 Cf. A001105, A005435, A259364, A259395, A259435.
%K A259563 sign,easy
%O A259563 0,3
%A A259563 _Vincenzo Librandi_, Jun 30 2015