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A052572
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E.g.f. (1+2x-2x^2)/(1-x)^2.
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5
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1, 4, 10, 36, 168, 960, 6480, 50400, 443520, 4354560, 47174400, 558835200, 7185024000, 99632332800, 1482030950400, 23538138624000, 397533007872000, 7113748561920000, 134449847820288000, 2676192208994304000
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OFFSET
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0,2
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COMMENTS
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a(n) equals the permanent of the (n+1) X (n+1) matrix whose entry directly below the entry in the top right corner is 3, and all of whose other entries are 1. [From John M. Campbell, May 25 2011]
In factorial base representation (A007623) the terms are written as: 1, 20, 120, 1200, 12000, 120000, ... From a(2) = 10 = "120" onward each term begins always with "120", followed by n-2 additional zeros. - Antti Karttunen, Sep 24 2016
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LINKS
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FORMULA
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E.g.f.: -(-2*x+2*x^2-1)/(-1+x)^2
Recurrence: {a(0)=1, a(1)=4, a(2)=10, (-n^2-5*n-4)*a(n)+(n+3)*a(n+1)=0}
a(n) = (n+3)*n! for n>0.
For n <= 1, a(n) = (n+1)^2, for n > 1, a(n) = (n+1)! + 2*n! - Antti Karttunen, Sep 24 2016
Sum_{n>=0} 1/a(n) = e - 4/3.
Sum_{n>=0} (-1)^n/a(n) = 8/3 - 5/e. (End)
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MAPLE
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spec := [S, {S=Prod(Union(Z, Z, Sequence(Z)), Sequence(Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[(1+2x-2x^2)/(1-x)^2, {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jul 03 2020 *)
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PROG
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(Scheme, two different implementations)
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CROSSREFS
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Row 7 of A276955, from a(2)=10 onward.
Cf. sequences with formula (n + k)*n! listed in A282466.
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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