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A075512
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Seventh column of triangle A075497.
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3
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1, 56, 1848, 47040, 1023792, 20076672, 365787136, 6314147840, 104637781248, 1680323893248, 26325099300864, 404403166003200, 6115019304300544, 91287994741981184, 1348582723009708032
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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(2*(m+1)*x)/6!.
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LINKS
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FORMULA
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a(n) = A075497(n+7, 7) = (2^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*2)^n/6!.
G.f.: 1/Product_{k=1..7} (1 - 2*k*x).
E.g.f.: (d^7/dx^7)(((exp(2*x)-1)/2)^7)/7! = (exp(2*x) - 384*exp(4*x) + 10935*exp(6*x) - 81920*exp(8*x) + 234375*exp(10*x) - 279936*exp(12*x) + 117649*exp(14*x))/6!.
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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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