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 A099962 #14 Mar 10 2023 05:39:12
%S A099962 1,1,1,1,2,3,5,13,28,64,207,578,1685,6518,22361,79319,357180,1453177,
%T A099962 6075215,31216968,146906126,707344776,4084254624,21823224623,
%U A099962 118932148555,762346849634,4559139897594,27742486678915,195472113041924
%N A099962 First column (also row sums) of triangle in A099961.
%p A099962 with(linalg):rev:=proc(a) local n, p; n:=vectdim(a): p:=i->a[n+1-i]: vector(n,p) end: ps:=proc(a) local n, q; n:=vectdim(a): q:=i->sum(a[j],j=1..i): vector(n,q) end: pss:=proc(a) local n, q; n:=vectdim(a): q:=proc(i) if i<=n then sum(a[j],j=1..i) else sum(a[j],j=1..n) fi end: vector(n+1,q) end: R[0]:=vector(1,1): for n from 1 to 35 do if n mod 3 = 0 or n mod 3 = 1 then R[n]:=ps(rev(R[n-1])) else R[n]:=pss(rev(R[n-1])) fi od: seq(R[n][1],n=0..35); # _Emeric Deutsch_, Nov 16 2004
%t A099962 r[n_] := r[n] = If[n == 0, {1}, Module[{a}, Join[a = Accumulate[Reverse[r[n-1]]], If[Mod[n, 3] == 2, {Last[a]}, {}]]]];
%t A099962 a[n_] := If[n == 0, 1, r[n][[1]]];
%t A099962 Table[a[n], {n, 0, 28}] (* _Jean-François Alcover_, Mar 10 2023 *)
%Y A099962 Cf. A099961.
%K A099962 nonn,easy
%O A099962 0,5
%A A099962 _N. J. A. Sloane_, Nov 13 2004
%E A099962 More terms from _Emeric Deutsch_, Nov 16 2004