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A081040
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5th binomial transform of (1,4,0,0,0,0,...).
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7
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1, 9, 65, 425, 2625, 15625, 90625, 515625, 2890625, 16015625, 87890625, 478515625, 2587890625, 13916015625, 74462890625, 396728515625, 2105712890625, 11138916015625, 58746337890625, 308990478515625, 1621246337890625
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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) = 10*a(n-1) - 25*a(n-2), a(0)=1, a(1)=9.
a(n) = (4n+5)*5^(n-1).
a(n) = Sum_{k=0..n} (k+1)*4^k*binomial(n, k).
G.f.: (1-x)/(1-5x)^2.
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MATHEMATICA
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CoefficientList[Series[(1 - x) / (1 - 5 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{10, -25}, {1, 9}, 30] (* Harvey P. Dale, Jan 10 2021 *)
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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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