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 A007695 Cardinalities of Sperner families on 1,...,n. (Formerly M2466) 6
 2, 3, 5, 10, 26, 96, 553, 5461, 100709, 3718354, 289725509, 49513793526, 19089032278261, 16951604697397302, 35231087224279091310, 173550485517380958360611, 2047581288200721764035942914 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Also number of f-vectors for simplicial complexes on at most n vertices. REFERENCES S. Johnson, Upper bounds for constant weight error correcting codes, Discrete Math., 3 (1972), 109-124. D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3 (p. 743). D. E. Knuth, Art of Computer Programming, Vol. 4, Section 7.3, to appear. S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS D. Knuth, Email to N. J. A. Sloane, Aug. 1994 Tamon Stephen and Timothy Yusun, Counting inequivalent monotone Boolean functions, arXiv preprint arXiv:1209.4623, 2012 MATHEMATICA c[ 0, 0 ]=1; c[ 0, 1 ]=1; kap[ 0, 0 ]=0; f[ n_ ] := Block[ {s=2, r, d, k, j}, For[ r=1, r<=n, r++, d=s; k=r; j=0; s=0; For[ x=0, x<=Binomial[ n, r ], x++, If[ x>=Binomial[ k, r ], k++, 0 ]; kap[ r, x ]=If[ x==0, 0, Binomial[ k-1, r-1 ]+kap[ r-1, x-Binomial[ k-1, r ] ] ]; While[ j

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Last modified January 17 23:09 EST 2021. Contains 340249 sequences. (Running on oeis4.)