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%I #12 Jun 13 2015 00:52:06
%S 12,72,300,1080,3612,11592,36300,111960,342012,1038312,3139500,
%T 9467640,28501212,85700232,257493900,773268120,2321377212,6967277352,
%U 20908123500,62736953400,188236026012,564758409672,1694375892300
%N O.g.f: -12*x^3/(-1+x)/(-1+2*x)/(-1+3*x) = -2-2/(-1+3*x)-6/(-1+x)+6/(-1+2*x) .
%C Negative of the determinant of a series of 3 X 3 matrices, related to Stirling's numbers of the second kind by a factor of 12 (cf. A000392, A028243).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F Let M = {{1, 1, 1}, {2^n, 4, 2}, {3^n, 9, 3}}. Then a(n) = -Det[M]
%F a(n) = 6*(1-2^n)+2*3^n = 12*A000392(n).
%t M = {{1, 1, 1}, {2^n, 4, 2}, {3^n, 9, 3}} a = Table[ -Det[M], {n, 3, 30}]
%Y Cf. A000392, A028243.
%K nonn,easy
%O 3,1
%A _Roger L. Bagula_, May 25 2006
%E Edited by _N. J. A. Sloane_, Dec 13 2007
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