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 A160181 Number of partitions of sets containing from 0 to n elements into blocks of at least 2 elements. 0
 1, 1, 2, 3, 7, 18, 59, 221, 936, 4361, 22083, 120336, 700653, 4333933, 28345090, 195233255, 1411303635, 10675375402, 84276173439, 692752181561, 5917018378496, 52416910416933, 480786834535247, 4559132648864256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums of A000296. 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. 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. LINKS Table of n, a(n) for n=0..23. FORMULA 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 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 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 MATHEMATICA 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 *) CROSSREFS Cf. A000296, A005001, A000110. Sequence in context: A032102 A100388 A186232 * A096203 A328430 A143874 Adjacent sequences: A160178 A160179 A160180 * A160182 A160183 A160184 KEYWORD easy,nonn AUTHOR Anonymous, May 03 2009 EXTENSIONS a(22)-a(23) corrected by Georg Fischer, Aug 28 2020 STATUS approved

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Last modified April 21 07:37 EDT 2024. Contains 371850 sequences. (Running on oeis4.)