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 A155862 #18 Sep 08 2022 08:45:41
%S A155862 1,4,22,130,790,4870,30274,189202,1186702,7461982,47007034,296527162,
%T A155862 1872479350,11833642006,74833075570,473463268642,2996771766046,
%U A155862 18974162475598,120167557286314,761214481604554,4822871486667526,30561172252753030,193682023673424226,1227594333811376050,7781431761074125486
%N A155862 A 'Morgan Voyce' transform of A007854.
%C A155862 Hankel transform is 3^n*2^binomial(n+1, 2).
%C A155862 Image of A007854 by Riordan array (1/(1-x), x/(1-x)^2).
%H A155862 Vincenzo Librandi, <a href="/A155862/b155862.txt">Table of n, a(n) for n = 0..200</a>
%F A155862 G.f.: 2/(3*sqrt(1-6*x+x^2) + x - 1).
%F A155862 G.f.: 1/(1 -x -3*x/(1 -x -x/(1 -x -x/(1 -x -x/(1 -x -x/(1- ... (continued fraction).
%F A155862 a(n) = Sum_{k=0..n} binomial(n+k, 2*k)*A007854(k) = Sum_{k=0..n} A085478(n,k) * A007854(k).
%F A155862 2*n*a(n) +(18-25*n)*a(n-1) + 41*(2*n-3)*a(n-2) +(57-25*n)*a(n-3) +2*(n-3)*a(n-4) =0. - _R. J. Mathar_, Nov 14 2011
%F A155862 a(n) ~ (1+3/sqrt(17)) * (13+3*sqrt(17))^n / 2^(2*n+2). - _Vaclav Kotesovec_, Feb 01 2014
%t A155862 CoefficientList[Series[2/(3*Sqrt[1-6*x+x^2]+x-1), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 01 2014 *)
%o A155862 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(3*Sqrt(1-6*x+x^2) +x -1) )); // _G. C. Greubel_, Jun 04 2021
%o A155862 (Sage)
%o A155862 def A155862_list(prec):
%o A155862 P.<x> = PowerSeriesRing(ZZ, prec)
%o A155862 return P( 2/(3*sqrt(1-6*x+x^2) +x-1) ).list()
%o A155862 A155862_list(30) # _G. C. Greubel_, Jun 04 2021
%Y A155862 Cf. A001850, A007854, A085478.
%K A155862 easy,nonn
%O A155862 0,2
%A A155862 _Paul Barry_, Jan 29 2009