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A060008
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a(n) = 9*binomial(n,4) = 3n*(n-1)*(n-2)*(n-3)/8.
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5
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0, 0, 0, 0, 9, 45, 135, 315, 630, 1134, 1890, 2970, 4455, 6435, 9009, 12285, 16380, 21420, 27540, 34884, 43605, 53865, 65835, 79695, 95634, 113850, 134550, 157950, 184275, 213759, 246645, 283185, 323640, 368280, 417384, 471240, 530145, 594405
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OFFSET
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0,5
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COMMENTS
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Number of permutations of n letters where exactly four change position.
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LINKS
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FORMULA
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Sum_{n>=4} 1/a(n) = 4/27.
Sum_{n>=4} (-1)^n/a(n) = 32*log(2)/9 - 64/27. (End)
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EXAMPLE
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a(6) = 135 since there are 15 ways to choose the four points that move and 9 ways to move them and 15*9 = 135.
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MATHEMATICA
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9*Binomial[Range[0, 40], 4] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 0, 0, 9}, 40] (* Harvey P. Dale, Jun 09 2014 *)
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PROG
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(PARI) { for (n=0, 1000, write("b060008.txt", n, " ", 3*n*(n - 1)*(n - 2)*(n - 3)/8); ) } \\ Harry J. Smith, Jul 01 2009
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CROSSREFS
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For changing 0, 1, 2, 3, 4, 5, n-4, n elements see A000012, A000004, A000217 (offset), A007290, A060008, A060836, A000475, A000166. Also see A000332, A008290.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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