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A016164
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Expansion of 1/((1-5x)(1-10x)).
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7
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1, 15, 175, 1875, 19375, 196875, 1984375, 19921875, 199609375, 1998046875, 19990234375, 199951171875, 1999755859375, 19998779296875, 199993896484375, 1999969482421875, 19999847412109375, 199999237060546875
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (5^n)*Stirling2(n+2, 2), n >= 0, with Stirling2(n, m) = A008277(n, m).
a(n) = -5^n + 2*10^n.
G.f.: 1/((1-5*x)*(1-10*x)).
E.g.f.: (d^2/dx^2)((((exp(5*x)-1)/5)^2)/2!) = -exp(5*x) + 2*exp(10*x).
Sum_{k=1..n} 5^(k-1)*5^(n-k)*binomial(n, k). - Zerinvary Lajos, Sep 24 2006
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MATHEMATICA
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LinearRecurrence[{15, -50}, {1, 15}, 20] (* Harvey P. Dale, Aug 08 2023 *)
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PROG
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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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