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A076013
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Seventh column of triangle A075504.
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4
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1, 252, 37422, 4286520, 419818707, 37047106404, 3037410645984, 235940417032320, 17594974122819093, 1271468563282273356, 89638618747098243186, 6196581962116572990600, 421646012618644954061559
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OFFSET
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0,2
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COMMENTS
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The e.g.f. given below is Sum_{m=0..6} (A075513(7,m)*exp(9*(m+1)*x))/6!.
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LINKS
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FORMULA
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a(n) = A075504(n+7, 7) = (9^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..6} (A075513(7, m)*((m+1)*9)^n)/6!.
G.f.: 1/Product_{k=1..7} (1 - 9*k*x).
E.g.f.: (d^7/dx^7)(((exp(9*x)-1)/9)^7)/7! = (exp(9*x) - 384*exp(18*x) + 10935*exp(27*x) - 81920*exp(36*x) + 234375*exp(45*x) - 279936*exp(54*x) + 117649*exp(63*x))/6!.
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MATHEMATICA
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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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STATUS
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approved
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