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 A155857 #26 Dec 23 2024 11:33:41
%S A155857 1,2,6,23,107,590,3786,27821,230869,2137978,21873854,245151555,
%T A155857 2987967551,39358156310,557259550034,8440866957273,136211005966889,
%U A155857 2333068710452146,42276699542130166,808068680469402095,16248405328930779027,342877404288485770718,7576652528705018522906
%N A155857 Row sums of triangle A155856.
%C A155857 For positive n, a(n) equals the permanent of the n X n matrix with 2's along the main diagonal and the upper diagonal, and 1's everywhere else. - _John M. Campbell_, Jul 09 2011
%H A155857 Vincenzo Librandi, <a href="/A155857/b155857.txt">Table of n, a(n) for n = 0..200</a>
%H A155857 Veronica Bitonti, Bishal Deb, and Alan D. Sokal, <a href="https://arxiv.org/abs/2412.10214">Thron-type continued fractions (T-fractions) for some classes of increasing trees</a>, arXiv:2412.10214 [math.CO], 2024. See p. 58.
%F A155857 G.f.: 1/(1 -x -x/(1 -x -x/(1 -x -2*x/(1 -x -2*x/(1 -x -3*x/(1 -x -3*x/(1 - ... (continued fraction);
%F A155857 a(n) = Sum_{k=0..n} binomial(2*n-k, k)*(n-k)!.
%F A155857 a(n) = Sum_{k=0..n} binomial(n+k, 2*k)*k!. - _Paul Barry_, May 28 2009
%F A155857 a(n) = (n+1)*a(n-1) -(n-3)*a(n-2) -a(n-3). - _R. J. Mathar_, Nov 15 2012
%F A155857 a(n) ~ exp(2) * n!. - _Vaclav Kotesovec_, Feb 08 2014
%t A155857 Table[Sum[Binomial[2*n-k,k]*(n-k)!,{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Feb 08 2014 *)
%o A155857 (Sage) [sum(binomial(2*n-k, k)*factorial(n-k) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Jun 05 2021
%Y A155857 Cf. A155856.
%K A155857 nonn,easy
%O A155857 0,2
%A A155857 _Paul Barry_, Jan 29 2009