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A245069 Number of Markov blanket structures with n labeled nodes. 1
1, 3, 15, 153, 3567, 196833, 25604415, 7727833473, 5321887813887, 8241841773665793, 28359559029362676735, 214672167825864945784833, 3545389677599343390373285887, 126865139766788531002690137546753, 9777654677248888055040528691642187775 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..78

Shyam Visweswaran and Gregory F. Cooper, Counting Markov blanket structures, arXiv:1407.2483 [stat.ML], 2014

FORMULA

a(1) = 1; for n > 1, a(n) = Sum_{q=0..n-1} Sum_{r=0..n-q-1} ((n-1)!/(q!*r!*s!))*2^(q*s)*2^(r*s) * A003024(s); n-1=q+r+s.

MATHEMATICA

(* b = A003024 *) b[0] = b[1] = 1; b[n_] := b[n] = Sum[-(-1)^k Binomial[n, k] 2^(k(n-k)) b[n-k], {k, 1, n}];

a[n_] := Sum[Sum[s = n-q-r-1; ((n-1)!/(q! r! s!)) 2^(q s) 2^(r s) b[s], {r, 0, n-q-1}], {q, 0, n 1}];

Array[a, 15] (* Jean-Fran├žois Alcover, Nov 28 2018 *)

CROSSREFS

Sequence in context: A293844 A181535 A162078 * A317667 A228901 A195226

Adjacent sequences:  A245066 A245067 A245068 * A245070 A245071 A245072

KEYWORD

nonn

AUTHOR

Shyam Visweswaran, Jul 10 2014

STATUS

approved

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Last modified June 23 11:29 EDT 2021. Contains 345397 sequences. (Running on oeis4.)