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A178759
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Expansion of 3*x*exp(x)*(exp(x)-1)^2
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0
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0, 0, 0, 18, 144, 750, 3240, 12642, 46368, 163350, 559800, 1881066, 6229872, 20406750, 66273480, 213759090, 685601856, 2188698150, 6959413080, 22053083514, 69672773520, 219535296750, 690106487400, 2164714299138, 6777100916064, 21179698653750, 66083277045240, 205880260458762
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OFFSET
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0,4
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COMMENTS
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a(n) is the sum of the digits in ternary sequences of length n, in which each element of the alphabet, {0,1,2} appears at least once in the sequence.
Generally, the E.g.f. for such sum of n-ary sequences (taken on an alphabet of {0,1,2,...,n-1}) is Binomial(n,2)*x*exp(x)*(exp(x)-1)^(n-1).
Cf. A058877 which is the sum of the digits in such binary sequences.
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LINKS
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Table of n, a(n) for n=0..27.
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FORMULA
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E.g.f.:3*x*exp(x)*(exp(x)-1)^2
a(n) = (3^n-3*2^n+3)*n - Mark van Hoeij, May 13 2013
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EXAMPLE
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a(3)=18 because there are six length 3 sequences on {0,1,2} that contain at least one 0, at least one 1 and at least one 2: (0,1,2),(0,2,1),(1,0,2),(1,2,0),(2,0,1),(2,1,0). The digits sum to 18.
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MATHEMATICA
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Range[0, 20]! CoefficientList[Series[3x Exp[x](Exp[x]-1)^2, {x, 0, 20}], x]
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PROG
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(PARI) x='x+O('x^66); concat([0, 0, 0], Vec(serlaplace(3*x*exp(x)*(exp(x)-1)^2))) \\ Joerg Arndt, May 13 2013
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CROSSREFS
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Cf. A178756.
Sequence in context: A127408 A008452 A126900 * A036397 A224329 A221352
Adjacent sequences: A178756 A178757 A178758 * A178760 A178761 A178762
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KEYWORD
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nonn
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AUTHOR
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Geoffrey Critzer, Dec 26 2010
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STATUS
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approved
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