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0, 3, 18, 81, 324, 1215, 4374, 15309, 52488, 177147, 590490, 1948617, 6377292, 20726199, 66961566, 215233605, 688747536, 2195382771, 6973568802, 22082967873, 69735688020, 219667417263, 690383311398, 2165293113021, 6778308875544
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OFFSET
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0,2
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COMMENTS
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If X_1,X_2,...,X_n is a partition of a 3n-set X into 3-blocks then, for n>0, a(n) is equal to the number of (n+1)-subsets of X intersecting each X_i (i=1,2,...,n). - Milan Janjic, Jul 21 2007
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LINKS
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FORMULA
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A trinomial transform. Differentiate (1+x+x^2)^n and set x=1.
a(n) = Sum_{i=0..n} Sum_{j=0..n} (2*n-2*i-j)*n!/(i!*j!*(n-i-j)!). (End)
a(n) = Sum_{k=0..2*n} T(n, k)*k, where T(n, k) is given by A027907.
a(n) = Sum_{k=0..n} Sum_{j=0..n} C(n, j)*C(j, k)*(j+k). (End)
G.f.: 3*x / (3*x-1)^2 .
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MAPLE
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MATHEMATICA
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nn=20; a=1/(1-3x); CoefficientList[Series[x D[ a, x] , {x, 0, nn}], x] (* Geoffrey Critzer, Nov 18 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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