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 A092365 #30 Dec 21 2024 22:30:14
%S A092365 1,8,36,112,275,576,1078,1856,2997,4600,6776,9648,13351,18032,23850,
%T A092365 30976,39593,49896,62092,76400,93051,112288,134366,159552,188125,
%U A092365 220376,256608,297136,342287,392400,447826,508928,576081,649672,730100,817776
%N A092365 Coefficient of X^2 in expansion of (1 + n*X + n*X^2)^n.
%H A092365 Vincenzo Librandi, <a href="/A092365/b092365.txt">Table of n, a(n) for n = 1..1000</a>
%H A092365 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A092365 a(n) = n^2*(binomial(n, 2) + 1).
%F A092365 G.f.: x*(1 + 3*x + 6*x^2 + 2*x^3)/(1-x)^5. [Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009; corrected by _R. J. Mathar_, Sep 16 2009]
%F A092365 From _Stefano Spezia_, Oct 08 2022: (Start)
%F A092365 E.g.f.: exp(x)*x*(2 + 6*x + 5*x^2 + x^3)/2.
%F A092365 a(n) = A000290(n)*A152947(n+1). (End)
%t A092365 Coefficient[Table[Expand[(1+n x+n x^2)^n],{n,60}],x,2] (* _Harvey P. Dale_, Mar 13 2011 *)
%t A092365 Table[n^2 (Binomial[n, 2] + 1), {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 8, 36, 112, 275}, 40] (* _Vincenzo Librandi_, Aug 15 2017 *)
%o A092365 (PARI) q(n)=(1+n*X+n*X^2)^n; for(i=1,40,print1(","polcoeff(q(i),2)))
%o A092365 (Magma) [n^2*(Binomial(n, 2)+1): n in [1..40]]; // _Vincenzo Librandi_, Aug 15 2017
%Y A092365 Cf. A000290, A152947.
%K A092365 nonn,easy
%O A092365 1,2
%A A092365 _Jon Perry_, Mar 19 2004