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 A317535 #9 Jan 25 2023 20:19:05
%S A317535 1,0,1,2,5,10,23,48,106,227,494,1065,2310,4991,10808,23376,50593,
%T A317535 109455,236858,512479,1108924,2399418,5191853,11233929,24307777,
%U A317535 52596430,113806948,246252376,532834797,1152933975,2494689316,5397944266,11679933875,25272740480,54684508281,118324934647
%N A317535 Expansion of 1/(1 + 1/(1 - x) - Product_{k>=1} 1/(1 - x^k)).
%C A317535 Invert transform of A000065.
%H A317535 Robert Israel, <a href="/A317535/b317535.txt">Table of n, a(n) for n = 0..2000</a>
%H A317535 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A317535 G.f.: 1/(1 - Sum_{k>=1} A000065(k)*x^k).
%p A317535 seq(coeff(series(1/(1+1/(1-x)-mul(1/(1-x^k),k=1..n)), x,n+1),x,n),n=0..40); # _Muniru A Asiru_, Jul 30 2018
%t A317535 nmax = 35; CoefficientList[Series[1/(1 + 1/(1 - x) - Product[1/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
%t A317535 nmax = 35; CoefficientList[Series[1/(1 - Sum[(PartitionsP[k] - 1) x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%t A317535 a[0] = 1; a[n_] := a[n] = Sum[(PartitionsP[k] - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 35}]
%Y A317535 Cf. A000041, A000065, A001970, A055887, A063834, A261049, A271619, A304966, A317536.
%K A317535 nonn
%O A317535 0,4
%A A317535 _Ilya Gutkovskiy_, Jul 30 2018