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 A369115 #7 Jan 22 2024 00:04:45
%S A369115 1,3,7,14,26,46,80,138,239,417,735,1309,2355,4275,7823,14416,26728,
%T A369115 49820,93300,175454,331170,627154,1191204,2268604,4330915,8286101,
%U A369115 15884857,30507175,58686513,113066033,218137531,421391695,814999229,1578000229,3058458885,5933549906
%N A369115 Expansion of (1 - x)^(-2) * Sum_{j>=0} (x^j / (1 - Sum_{k=1..j} x^k)).
%C A369115 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 A369115 Partial sums of A186537 starting at n = 1.
%p A369115 gf := (1 - x)^(-2) * add(x^j / (1 - add(x^k, k = 1..j)), j = 0..42):
%p A369115 ser := series(gf, x, 40): seq(coeff(ser, x, k), k = 0..38);
%Y A369115 Cf. This sequence (n=-2), A186537 left shifted (n=-1), A079500 (n=0), A368279 (n=1), A369116 (n=2).
%K A369115 nonn
%O A369115 0,2
%A A369115 _Peter Luschny_, Jan 21 2024