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 A006897 Hierarchical linear models on n factors allowing 2-way interactions; or graphs with <= n nodes. (Formerly M1153) 3
 1, 2, 4, 8, 19, 53, 209, 1253, 13599, 288267, 12293435, 1031291299, 166122463891, 50668153831843, 29104823811067331, 31455590793615376099, 64032471295321173271027, 245999896624828253856990803, 1787823725042236528801735181651, 24639597076850046760911809226614419 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The subsequence of primes begins: 2, 19, 53, 166122463891, 29104823811067331. - Jonathan Vos Post, Feb 14 2010 a(n) is the number of isolated points over all simple unlabelled graphs with (n+1) nodes. - Geoffrey Critzer, Apr 14 2012 REFERENCES R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..87 FORMULA O.g.f.: A(x)/(1-x) where A(x) is o.g.f. for A000088. - Geoffrey Critzer, Apr 12 2012 EXAMPLE a(2)=4 includes null graph [], G1=[o], G2=[o o], G3=[o-o]. MAPLE b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(ceil((p[j]-1)/2)       +add(igcd(p[k], p[j]), k=1..j-1), j=1..nops(p)))([l[], 1\$n])),        add(b(n-i*j, i-1, [l[], i\$j])/j!/i^j, j=0..n/i))     end: a:= proc(n) option remember; b(n\$2, [])+`if`(n>0, a(n-1), 0) end: seq(a(n), n=0..20);  # Alois P. Heinz, Aug 14 2019 MATHEMATICA nn = 15; g = Sum[NumberOfGraphs[n] x^n, {n, 0, nn}]; CoefficientList[Series[g/(1 - x), {x, 0, nn}], x]  (* Geoffrey Critzer, Apr 12 2012 *) CROSSREFS Partial sums of A000088. Sequence in context: A173310 A320178 A128816 * A287025 A034767 A005518 Adjacent sequences:  A006894 A006895 A006896 * A006898 A006899 A006900 KEYWORD easy,nonn,nice AUTHOR STATUS approved

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)