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 A277395 #19 Feb 13 2020 11:54:15
%S A277395 1,3,9,33,145,713,3745,20513,115713,667329,3916033,23305857,140327681,
%T A277395 853262465,5231925761,32313686529,200843829249,1255308123137,
%U A277395 7884792852481,49745076576257,315091155558401,2003009460686849,12774610185633793
%N A277395 a(n) = Sum_{k=0..n} binomial(n+1,k+1)*A001003(k).
%F A277395 G.f.: (1-sqrt(8*x^2-8*x+1))/(4*(1-x)^2*x).
%F A277395 D-finite with recurrence: (n+1)*a(n) +2*(-5*n+1)*a(n-1) +(25*n-23)*a(n-2) +12*(-2*n+3)*a(n-3) +8*(n-2)*a(n-4)=0. - _R. J. Mathar_, Mar 12 2017
%p A277395 f := gfun:-rectoproc({(n + 1)*a(n) + 2*(-5*n + 1)*a(n - 1) + (25*n - 23)*a(n - 2) + 12*(-2*n + 3)*a(n - 3) + 8*(n - 2)*a(n - 4) = 0, a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 33}, a(n), remember); map(f, [$ (0 .. 20)]); # _Georg Fischer_, Feb 13 2020
%o A277395 (Maxima)
%o A277395 g(k):=1/(k+1)*sum((-1)^j*2^(k-j)*binomial(k+1,j)*binomial(2*k-j,k),j,0,k);
%o A277395 makelist(sum(binomial(n+1,k+1)*g(k),k,0,n),n,0,23);
%Y A277395 Cf. A001003.
%K A277395 nonn
%O A277395 0,2
%A A277395 _Vladimir Kruchinin_, Oct 12 2016