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A028244
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a(n) = 4^(n-1) - 3*3^(n-1) + 3*2^(n-1) - 1 (essentially Stirling numbers of second kind).
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19
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0, 0, 0, 6, 60, 390, 2100, 10206, 46620, 204630, 874500, 3669006, 15195180, 62350470, 254135700, 1030793406, 4166023740, 16792841910, 67558001700, 271392695406, 1089054420300, 4366671742950, 17498055448500, 70086339807006
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OFFSET
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1,4
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COMMENTS
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For n>=4, a(n) is equal to the number of functions f: {1,2,...,n-1}->{1,2,3,4} such that Im(f) contains 3 fixed elements. - Aleksandar M. Janjic and Milan Janjic, Feb 27 2007
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LINKS
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FORMULA
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G.f.: 6x^4/((1-x)(1-2x)(1-3x)(1-4x)). - R. J. Mathar, Oct 23 2008
E.g.f.: (exp(4*x) - 4*exp(3*x) + 6*exp(2*x) - 4*exp(x) + 1)/4, with a(0) = 0. - Wolfdieter Lang, May 03 2017
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MATHEMATICA
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Table[4^(n - 1) - 3*3^(n - 1) + 3*2^(n - 1) - 1, {n, 1, 30}] (* Stefan Steinerberger, Apr 13 2006 *)
Table[6*StirlingS2[n, 4], {n, 1, 30}] (* G. C. Greubel, Nov 19 2017 *)
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PROG
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(Magma) [4^(n-1) - 3*3^(n-1) + 3*2^(n-1) - 1: n in [1..30]]; // G. C. Greubel, Nov 19 2017
(PARI) for(n=1, 30, print1(6*stirling(n, 4, 2), ", ")) \\ G. C. Greubel, Nov 19 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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