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 A027178 #27 Feb 17 2016 16:21:54 %S A027178 1,6,20,52,120,260,544,1116,2264,4564,9168,18380,36808,73668,147392, %T A027178 294844,589752,1179572,2359216,4718508,9437096,18874276,37748640, %U A027178 75497372,150994840,301989780,603979664,1207959436,2415918984 %N A027178 a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A027170. %C A027178 Define a triangle U(n,k) with U(n,0) = n*(n+1) + 1 for n>=0 and U(r,c) = U(r-1,c-1) + U(r-1,c). The sum of the terms in row n is a(n). The first rows are 1; 3, 3; 7, 6, 7; 13, 13, 13, 13; 21, 26, 26, 26, 21; row sums are 1, 6, 20, 52, 120. - _J. M. Bergot_, Feb 15 2013 %C A027178 This triangle is now A222405. - _N. J. A. Sloane_, Feb 18 2013 %F A027178 a(n) = 9*2^n - 4n - 8 (conjectured). - _Ralf Stephan_, Feb 13 2004 %F A027178 Conjectures from _Colin Barker_, Feb 17 2016: (Start) %F A027178 a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3) for n>2. %F A027178 G.f.: (1+x)^2 / ((1-x)^2*(1-2*x)). %F A027178 (End) %Y A027178 Cf. A222405. %K A027178 nonn %O A027178 0,2 %A A027178 _Clark Kimberling_