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A081911
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a(n) = 5^n*(n^2 - n + 50)/50.
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4
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1, 5, 26, 140, 775, 4375, 25000, 143750, 828125, 4765625, 27343750, 156250000, 888671875, 5029296875, 28320312500, 158691406250, 885009765625, 4913330078125, 27160644531250, 149536132812500, 820159912109375
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A081910 5th binomial transform of (1,0,1,0,0,0,...). Case k=5 where a(n,k) = k^n*(n^2 - n + 2k^2)/(2k^2) with g.f. (1 - 2kx + (k^2+1)x^2)/(1-kx)^3.
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LINKS
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FORMULA
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a(n) = 5^n*(n^2 - n + 50)/50.
G.f.: (1 - 10x + 26x^2)/(1-5x)^3.
a(n) = 15*a(n-1) - 75*a(n-2) + 125*a(n-3); a(0)=1, a(1)=5, a(2)=26. - _Harvey P. Dale, Jul 22 2011
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MATHEMATICA
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Table[5^n(n^2-n+50)/50, {n, 0, 20}] (* or *) LinearRecurrence[{15, -75, 125}, {1, 5, 26}, 20] (* Harvey P. Dale, Jul 22 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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