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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

N. J. A. Sloane, Colin Mallows, Simon Plouffe

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.)