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A081911
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| Vincenzo Librandi, Table of n, a(n) for n = 0..150
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FORMULA
| a(n)=5^n(n^2-n+50)/50 G.f.: (1-10x+26x^2)/(1-5x)^3
a(0)=1, a(1)=5, a(2)=26, a(n)=15*a(n-1)-75*a(n-2)+125*a(n-3) [From Harvey P. Dale, Jul 22 2011]
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MATHEMATICA
| Table[5^n(n^2-n+50)/50, {n, 0, 20}] (* or *) LinearRecurrence[{15, -75, 125}, {1, 5, 26}, 20] (* From Harvey P. Dale, Jul 22 2011 *)
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PROG
| (MAGMA) [5^n*(n^2-n+50)/50: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011
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CROSSREFS
| Cf. A081912.
Sequence in context: A035029 A081569 A005573 * A081187 A104498 A045379
Adjacent sequences: A081908 A081909 A081910 * A081912 A081913 A081914
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 31 2003
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