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 A172383 #24 Jun 04 2022 09:42:09
%S A172383 1,1,1,2,4,8,19,46,118,322,903,2653,8053,25194,81387,269667,917529,
%T A172383 3197480,11393821,41497060,154186653,584151512,2254240317,8852998343,
%U A172383 35361762709,143540660088,591802631729,2476701062087
%N A172383 a(0)=1, otherwise a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-k-1,k)*a(n-1-2*k).
%H A172383 Seiichi Manyama, <a href="/A172383/b172383.txt">Table of n, a(n) for n = 0..932</a>
%F A172383 G.f. A(x) satisfies: A(x) = 1 + (x/(1-x^2)) * A(x/(1-x^2)).
%e A172383 Eigensequence for number triangle
%e A172383 1;
%e A172383 1, 0;
%e A172383 0, 1, 0;
%e A172383 1, 0, 1, 0;
%e A172383 0, 2, 0, 1, 0;
%e A172383 1, 0, 3, 0, 1, 0;
%e A172383 0, 3, 0, 4, 0, 1, 0;
%e A172383 1, 0, 6, 0, 5, 0, 1, 0;
%e A172383 0, 4, 0, 10, 0, 6, 0, 1, 0;
%e A172383 1, 0, 10, 0, 15, 0, 7, 0, 1, 0;
%e A172383 0, 5, 0, 20, 0, 21, 0, 8, 0, 1, 0;
%e A172383 (augmented version of Riordan array (1/(1-x^2), x/(1-x^2)), A030528.
%p A172383 A172383 := proc(n)
%p A172383 option remember;
%p A172383 if n = 0 then
%p A172383 1;
%p A172383 else
%p A172383 add(binomial(n-k-1,k)*procname(n-1-2*k),k=0..floor((n-1)/2)) ;
%p A172383 end if;
%p A172383 end proc:
%p A172383 seq(A172383(n),n=0..20) ; # _R. J. Mathar_, Feb 11 2015
%t A172383 a[n_]:= If[n == 0, 1, Sum[Binomial[n-k-1, k]*a[n-2*k-1], {k, 0, Floor[(n-1)/2]}]]; Table[a[n], {n, 0, 30}] (* _G. C. Greubel_, Oct 07 2018 *)
%Y A172383 Cf. A030528.
%K A172383 easy,nonn
%O A172383 0,4
%A A172383 _Paul Barry_, Feb 01 2010
%E A172383 Name corrected by _R. J. Mathar_, Feb 11 2015