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A075910
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Seventh column of triangle A075499.
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2
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1, 112, 7392, 376320, 16380672, 642453504, 23410376704, 808210923520, 26787271999488, 860325833342976, 26956901684084736, 828217683974553600, 25047119070415028224, 747831252926309859328, 22095179333791056396288
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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(4*(m+1)*x)/6!.
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LINKS
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FORMULA
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a(n) = A075499(n+7, 7) = (4^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*4)^n/6!.
G.f.: 1/Product_{k=1..7} (1 - 4*k*x).
E.g.f.: (d^7/dx^7)(((exp(4*x)-1)/4)^7)/7! = (exp(4*x) - 384*exp(8*x) + 10935*exp(12*x) - 81920*exp(16*x) + 234375*exp(20*x) - 279936*exp(24*x) + 117649*exp(28*x))/6!.
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MATHEMATICA
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CoefficientList[Series[1/Product[1-4k x, {k, 7}], {x, 0, 20}], x] (* Harvey P. Dale, Aug 11 2021 *)
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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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