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 A160181 #21 Aug 28 2020 06:16:31
%S A160181 1,1,2,3,7,18,59,221,936,4361,22083,120336,700653,4333933,28345090,
%T A160181 195233255,1411303635,10675375402,84276173439,692752181561,
%U A160181 5917018378496,52416910416933,480786834535247,4559132648864256
%N A160181 Number of partitions of sets containing from 0 to n elements into blocks of at least 2 elements.
%C A160181 Partial sums of A000296.
%C A160181 a(n) is the total number of complete rhyme schemes for 0 to n lines; in other words, a(n) is the total number of rhyme schemes for 0 to n lines where each line rhymes with at least one other line.
%C A160181 If the restriction that the blocks of the partitions must have at least 2 elements is removed, then A005001 is obtained except for the first term of A005001.
%F A160181 G.f.: (G(0)-1)/(1-x) where G(k) = 1 + (1-x)/(1+x-x*k)/(1-x/(x+(1-x)/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jan 21 2013
%F A160181 G.f.: T(0)/(1-x), where T(k) = 1 - x^2*(k+1)/( x^2*(k+1) - (1-x*k)*(1-x-x*k)/T(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Oct 19 2013
%F A160181 G.f.: (1+x*sum{k>=0, x^k/prod[p=0..k, 1-p*x]})/(1-x^2). - _Sergei N. Gladkovskii_, Jan 25 2014
%t A160181 m=30; CoefficientList[Series[(1+x*Sum[x^k/Product[1-p*x, {p,0,k}], {k,0,m}])/(1-x^2), {x, 0,m}], x] (* _Georg Fischer_, Aug 28 2020 *)
%Y A160181 Cf. A000296, A005001, A000110.
%K A160181 easy,nonn
%O A160181 0,3
%A A160181 Anonymous, May 03 2009
%E A160181 a(22)-a(23) corrected by _Georg Fischer_, Aug 28 2020