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A006896
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Number of hierarchical linear models on n factors allowing 2-way interactions; or labeled graphs on <= n nodes.
(Formerly M1520)
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7
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1, 2, 5, 18, 113, 1450, 40069, 2350602, 286192513, 71213783666, 35883905263781, 36419649682706466, 74221659280476136241, 303193505953871645562970, 2480118046704094643352358501, 40601989176407026666590990422106
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| 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.
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MAPLE
| A006896 := proc(n) local k; 1+binomial(n, 1)+sum(binomial(n, k)*2^(1/2*k*(k-1)), k = 2 .. n) end;
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PROG
| (PARI) a(n)=sum(k=0, n, binomial(n, k)*2^((k^2-k)/2))
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CROSSREFS
| a(n)=1+A004140(n).
Sequence in context: A174122 A005805 A058338 * A125625 A097584 A197855
Adjacent sequences: A006893 A006894 A006895 * A006897 A006898 A006899
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KEYWORD
| easy,nonn,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), C. L. Mallows (colinm(AT)research.avayalabs.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Error in formula line corrected Sep 15 1997 (thanks to R. K. Guy for pointing this out)
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