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 A369116 #8 Jan 22 2024 00:04:51
%S A369116 1,-1,1,0,1,1,3,4,9,15,29,53,100,186,352,663,1257,2387,4547,8678,
%T A369116 16602,31818,61092,117486,226277,436403,842731,1629297,3153466,
%U A369116 6109704,11848634,22998892,44680016,86869392,169024094,329110519,641254825,1250261783,2439155631
%N A369116 Expansion of (1 - x)^2 * Sum_{j>=0} (x^j / (1 - Sum_{k=1..j} x^k)).
%C A369116 Considering more generally the family of generating functions (1 - x)^n * Sum_{j>=0} (x^j / (1 - Sum_{k=1..j} x^k)) one finds several sequences related to compositions as indicated in the cross-references.
%F A369116 a(n) = A368279(n) - A368279(n-1) where A368279(-1) = 0.
%p A369116 gf := (1 - x)^2 * add(x^j / (1 - add(x^k, k = 1..j)), j = 0..42):
%p A369116 ser := series(gf, x, 40): seq(coeff(ser, x, k), k = 0..38);
%Y A369116 Cf. A369115 (n=-2), A186537 left shifted (n=-1), A079500 (n=0), A368279 (n=1), this sequence (n=2).
%K A369116 sign
%O A369116 0,7
%A A369116 _Peter Luschny_, Jan 21 2024