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A066534
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Total number of walks with length > 0 in the Hasse diagram of a Boolean algebra of order n.
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5
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0, 1, 6, 30, 152, 840, 5232, 37072, 297600, 2680704, 26812160, 294945024, 3539364864, 46011796480, 644165265408, 9662479226880, 154599668154368, 2628194359738368, 47307498477649920, 898842471080329216
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Let P(A) be the power set of an n-element set A. Then a(n) = the total number of ways to add 1 or more elements of A to each element x of P(A) where the elements to add are not elements of x and order of addition is important. - Ross La Haye (rlahaye(AT)new.rr.com), Nov 19 2007
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
Eric Weisstein, Walk
Eric Weisstein, Boolean Algebra
Eric Weisstein, Hasse Diagram
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FORMULA
| a(n)=n!*Sum_{i+j<n, i, j >= 0} 1/(i!*j!). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 01 2002
E.g.f.: x*exp(2*x)/(1-x). a(n) = n*(a(n-1)+2^(n-1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 29 2003
a(n) = Sum[(n! / k!) * 2^k {k=0 to n-1}] = Sum[P(n, n-k) * 2^k {k=0 to n-1}] = n! * Sum[2^k / k! {k=0 to n-1}] = Sum[P(n, k) * 2^(n-k) {k=1 to n}] = sum of the n-th row of A090802 from column 1 on = A010842(n) - 2^n = n * A010842(n-1) = binomial transform of A007526 - Ross La Haye (rlahaye(AT)new.rr.com), Sep 15 2004
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EXAMPLE
| a(2) = 6 because (2! / 0! * 2^0) + (2! / 1! * 2^1) = 6
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MATHEMATICA
| a[ n_ ] := n!Sum[ 2^k/k!, {k, 0, n-1} ]
Table[n*Gamma[n, 2]*E^2, {n, 0, 19}] (Ross La Haye (rlahaye(AT)new.rr.com), Oct 09 2005)
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CROSSREFS
| Cf. A010842, A067273, A090802, A007526.
Sequence in context: A054117 A033132 A022023 * A126474 A127017 A152224
Adjacent sequences: A066531 A066532 A066533 * A066535 A066536 A066537
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KEYWORD
| easy,nonn,nice,walk
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AUTHOR
| Peter Bertok (peter(AT)bertok.com), Jan 07 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 12, 2002.
Entry revised by Ross La Haye (rlahaye(AT)new.rr.com), Aug 18 2006
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