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 A213757 #21 Feb 19 2024 04:07:08 %S A213757 1,14,65,214,597,1518,3649,8462,19157,42646,93777,204294,441781, %T A213757 949598,2030849,4324510,9174069,19397574,40893265,85981910,180353621, %U A213757 377485774,788527425,1644165294,3422550037,7113537398,14763947729 %N A213757 Principal diagonal of the convolution array A213756. %H A213757 Clark Kimberling, <a href="/A213757/b213757.txt">Table of n, a(n) for n = 1..100</a> %H A213757 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-19,25,-16,4). %F A213757 a(n) = -2 + 2^(n+1) - 6*n + n*2^(n+2) - 3*n^2. %F A213757 a(n) = 7*a(n-1) - 19*a(n-2) + 25*a(n-3) - 16*a(n-4) + 4*a(n-5). %F A213757 G.f.: f(x)/g(x), where f(x) = x*(1 + 7*x - 14*x^2) and g(x) = (1 - 2*x)^2 (1 - x)^3. %t A213757 (See A213756.) %Y A213757 Cf. A213756, A213500. %K A213757 nonn,easy %O A213757 1,2 %A A213757 _Clark Kimberling_, Jun 20 2012