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Search: id:A081038
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| A081038 |
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3rd binomial transform of (1,2,0,0,0,0,0,0....). |
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+0
10
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| 1, 5, 21, 81, 297, 1053, 3645, 12393, 41553, 137781, 452709, 1476225, 4782969, 15411789, 49424013, 157837977, 502211745, 1592728677, 5036466357, 15884240049, 49977243081, 156905298045, 491636600541, 1537671920841
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n)=6*a(n-1)-9*a(n-2), with a(0)=1, a(1)=5; a(n)=(2n+3)3^(n-1); a(n)=Sum {k=0..n, (k+1)*2^k Binomial(n, k)}; g.f.: (1-x)/(1-3x)^2
Equals 2*A086972(n) - 1. - Lambert Herrgesell (zero815(AT)googlemail.com), Feb 10 2008
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MAPLE
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a:=n->sum (3^n*n^binomial(j, n)/27, j=1..n): seq(a(n), n=2..25); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 18 2009]
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CROSSREFS
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Cf. A001792, A081039, A081040.
First differences of A027471.
Sequence in context: A108863 A027172 A029870 this_sequence A153008 A051196 A094834
Adjacent sequences: A081035 A081036 A081037 this_sequence A081039 A081040 A081041
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 03 2003
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