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%I #43 Sep 08 2022 08:44:50
%S 0,0,0,6,60,390,2100,10206,46620,204630,874500,3669006,15195180,
%T 62350470,254135700,1030793406,4166023740,16792841910,67558001700,
%U 271392695406,1089054420300,4366671742950,17498055448500,70086339807006
%N a(n) = 4^(n-1) - 3*3^(n-1) + 3*2^(n-1) - 1 (essentially Stirling numbers of second kind).
%C 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
%H Seiichi Manyama, <a href="/A028244/b028244.txt">Table of n, a(n) for n = 1..1661</a>
%H K. S. Immink, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.299.4608">Coding Schemes for Multi-Level Channels that are Intrinsically Resistant Against Unknown Gain and/or Offset Using Reference Symbols</a>, Electronics Letters ( Volume: 50, Issue: 1, January 2 2014 ).
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%F a(n) = 6*S(n, 4) = 6*A000453(n). - _Emeric Deutsch_, May 02 2004
%F G.f.: 6x^4/((1-x)(1-2x)(1-3x)(1-4x)). - _R. J. Mathar_, Oct 23 2008
%F 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
%F a(n) = 2*A032263(n). - _Alois P. Heinz_, Jan 24 2018
%t Table[4^(n - 1) - 3*3^(n - 1) + 3*2^(n - 1) - 1, {n, 1, 30}] (* _Stefan Steinerberger_, Apr 13 2006 *)
%t Table[6*StirlingS2[n,4], {n,1,30}] (* _G. C. Greubel_, Nov 19 2017 *)
%o (Magma) [4^(n-1) - 3*3^(n-1) + 3*2^(n-1) - 1: n in [1..30]]; // _G. C. Greubel_, Nov 19 2017
%o (PARI) for(n=1,30, print1(6*stirling(n,4,2), ", ")) \\ _G. C. Greubel_, Nov 19 2017
%Y Cf. A000453, A008277, A032263, A163626.
%K nonn
%O 1,4
%A _N. J. A. Sloane_, Doug McKenzie (mckfam4(AT)aol.com)
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