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 A360149 #25 Mar 02 2023 09:35:51
%S A360149 1,2,7,27,107,429,1731,7012,28478,115864,471991,1924483,7852083,
%T A360149 32053208,130893949,534673600,2184482707,8926392419,36479840422,
%U A360149 149095843951,609400587426,2490900041118,10181669553847,41618414303969,170118507902985,695366323719302
%N A360149 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k,n-2*k).
%F A360149 G.f.: 1 / ( sqrt(1-4*x) * (1 - x^2 * c(x)^5) ), where c(x) is the g.f. of A000108.
%F A360149 a(n) ~ sqrt((7 - 5*(2/(173 + 21*sqrt(69)))^(1/3) + ((173 + 21*sqrt(69))/2)^(1/3)) / 69) / ((4 - (2/(25 - 3*sqrt(69)))^(1/3) - ((25 - 3*sqrt(69))/2)^(1/3))/3)^n. - _Vaclav Kotesovec_, Jan 28 2023
%F A360149 D-finite with recurrence n*(47*n-1011)*a(n) +(-261*n^2 +8567*n -6378)*a(n-1) +2*(-165*n^2 -9388*n +16143)*a(n-2) +(3089*n^2 +919*n -27492)*a(n-3) +2*(-1283*n^2 +3900*n +3981)*a(n-4) +4*(81*n+11)*(2*n-9)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2023
%p A360149 A360149 := proc(n)
%p A360149 add(binomial(2*n+k,n-2*k),k=0..floor(n/2)) ;
%p A360149 end proc:
%p A360149 seq(A360149(n),n=0..40) ; # _R. J. Mathar_, Mar 02 2023
%t A360149 a[n_] := Sum[Binomial[2*n + k, n - 2*k], {k, 0, Floor[n/2]}]; Array[a, 26, 0] (* _Amiram Eldar_, Jan 28 2023 *)
%o A360149 (PARI) a(n) = sum(k=0, n\2, binomial(2*n+k, n-2*k));
%o A360149 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1-x^2*(2/(1+sqrt(1-4*x)))^5)))
%Y A360149 Cf. A014300, A106188, A108081, A114121, A176287.
%Y A360149 Cf. A000108, A360144, A360150.
%K A360149 nonn
%O A360149 0,2
%A A360149 _Seiichi Manyama_, Jan 28 2023