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A118979
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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) .
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0
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12, 72, 300, 1080, 3612, 11592, 36300, 111960, 342012, 1038312, 3139500, 9467640, 28501212, 85700232, 257493900, 773268120, 2321377212, 6967277352, 20908123500, 62736953400, 188236026012, 564758409672, 1694375892300
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OFFSET
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3,1
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COMMENTS
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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).
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LINKS
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FORMULA
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Let M = {{1, 1, 1}, {2^n, 4, 2}, {3^n, 9, 3}}. Then a(n) = -Det[M]
a(n) = 6*(1-2^n)+2*3^n = 12*A000392(n).
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MATHEMATICA
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M = {{1, 1, 1}, {2^n, 4, 2}, {3^n, 9, 3}} a = Table[ -Det[M], {n, 3, 30}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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