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 A360211 #14 Mar 02 2023 09:38:37
%S A360211 1,2,5,17,61,221,812,3021,11344,42899,163146,623320,2390653,9198879,
%T A360211 35494701,137290466,532149805,2066501909,8038146035,31312535610,
%U A360211 122140123201,477002869614,1864912495716,7298427590543,28588888586743,112080607196843,439744801379594
%N A360211 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-3*k,n-2*k).
%F A360211 G.f.: 1 / ( sqrt(1-4*x) * (1 + x^2 * c(x)) ), where c(x) is the g.f. of A000108.
%F A360211 a(n) ~ 2^(2*n+3) / (9*sqrt(Pi*n)). - _Vaclav Kotesovec_, Feb 18 2023
%F A360211 D-finite with recurrence 2*n*a(n) +(-5*n+2)*a(n-1) +(-11*n+12)*a(n-2) +2*(-n+5)*a(n-3) +(-7*n+2)*a(n-4) +2*(-2*n+5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2023
%p A360211 A360211 := proc(n)
%p A360211 add((-1)^k*binomial(2*n-3*k,n-2*k),k=0..floor(n/2)) ;
%p A360211 end proc:
%p A360211 seq(A360211(n),n=0..40) ; # _R. J. Mathar_, Mar 02 2023
%o A360211 (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n-3*k, n-2*k));
%o A360211 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1+2*x^2/(1+sqrt(1-4*x)))))
%Y A360211 Cf. A005317, A024718, A176332, A360185.
%Y A360211 Cf. A000108, A176287.
%Y A360211 Cf. A026641, A360212.
%K A360211 nonn
%O A360211 0,2
%A A360211 _Seiichi Manyama_, Jan 30 2023