

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
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OFFSET

0,3


COMMENTS

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



FORMULA

G.f.: (G(0)1)/(1x) where G(k) = 1 + (1x)/(1+xx*k)/(1x/(x+(1x)/G(k+1) )); (continued fraction).  Sergei N. Gladkovskii, Jan 21 2013
G.f.: T(0)/(1x), where T(k) = 1  x^2*(k+1)/( x^2*(k+1)  (1x*k)*(1xx*k)/T(k+1) ); (continued fraction).  Sergei N. Gladkovskii, Oct 19 2013


MATHEMATICA

m=30; CoefficientList[Series[(1+x*Sum[x^k/Product[1p*x, {p, 0, k}], {k, 0, m}])/(1x^2), {x, 0, m}], x] (* Georg Fischer, Aug 28 2020 *)


CROSSREFS



KEYWORD

easy,nonn


AUTHOR

Anonymous, May 03 2009


EXTENSIONS



STATUS

approved



