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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| f 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 R. Janjic (agnus(AT)blic.net), Jul 21 2007.
Sum{n>0,1/a(n)} = ln(3/2) = 0.405465108... = A016578. - Franz Vrabec, Jan 07 2012
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LINKS
| Milan Janjic, Two Enumerative Functions
Index to sequences with linear recurrences with constant coefficients, signature (6,-9).
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FORMULA
| A trinomial transform. Differentiate (1+x+x^2)^n and set x=1. a(n)=sum{i=0..n, sum{j=0..n, (2n-2i-j)*n!/(i!j!(n-i-j)!)}} - Paul Barry (pbarry(AT)wit.ie), Feb 06 2004
a(n)=sum{k=0..2n, 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)}}. - Paul Barry (pbarry(AT)wit.ie), Feb 15 2005
G.f. 3*x / (3*x-1)^2 . a(n) = 3*A027471(n+1). - R. J. Mathar, Jun 19 2011
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MAPLE
| A036290 := proc(n) n*3^n ; end proc: # R. J. Mathar, Jun 18 2011
with(finance):seq(add(futurevalue( 3, 2, n), k=0..n), n=-1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008
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PROG
| (PARI) a(n)=3^n*n \\ Charles R Greathouse IV, Jun 18, 2011
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CROSSREFS
| Cf. A006234.
Sequence in context: A056310 A135371 A086346 * A078904 A099012 A122069
Adjacent sequences: A036287 A036288 A036289 * A036291 A036292 A036293
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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