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 A006896 Number of hierarchical linear models on n factors allowing 2-way interactions; or labeled graphs on <= n nodes. (Formerly M1520) 8
 1, 2, 5, 18, 113, 1450, 40069, 2350602, 286192513, 71213783666, 35883905263781, 36419649682706466, 74221659280476136241, 303193505953871645562970, 2480118046704094643352358501, 40601989176407026666590990422106, 1329877330167226219547875498464516481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES P. De Causmaecker, S. De Wannemacker, Decomposition of Intervals in the Space of Anti-Monotonic Functions, in Manuel Ojeda-Aciego, Jan Outrata (Eds.): CLA 2013, pp. 57{67, ISBN 9782746665668, Laboratory L3i, University of La Rochelle, 2013; http://ceur-ws.org/Vol-1062/proceedings-cla2013.pdf#page=69. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..80 Patrick De Causmaecker, Stefan De Wannemacker, On the number of antichains of sets in a finite universe, arXiv:1407.4288 [math.CO], 2014 FORMULA a(n) = 1 + C(n, 1) + C(n, 2)*2 + C(n, 3)*2^3 + C(n, 4)*2^6 + ... + C(n, n)*2^(n*(n-1)/2). E.g.f.: exp(x)*A(x) where A(x) is e.g.f. for A006125. - Geoffrey Critzer, Apr 11 2012. MAPLE A006896 := proc(n) local k; 1+binomial(n, 1) +add(binomial(n, k)*2^(1/2*k*(k-1)), k = 2 .. n) end; seq (A006896(n), n=0..20); MATHEMATICA nn=20; g=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[Exp[x]g, {x, 0, nn}], x]  (*Geoffrey Critzer, Apr 11 2012*) PROG (PARI) a(n)=sum(k=0, n, binomial(n, k)*2^((k^2-k)/2)) CROSSREFS a(n) = 1+A004140(n). Sequence in context: A174122 A005805 A058338 * A125625 A281532 A097584 Adjacent sequences:  A006893 A006894 A006895 * A006897 A006898 A006899 KEYWORD easy,nonn,nice AUTHOR EXTENSIONS Error in formula line corrected Sep 15 1997 (thanks to R. K. Guy for pointing this out) STATUS approved

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)