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Search: id:A075271
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| A075271 |
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a(0)=1 and, for n>=1, (BM)a(n)=2a(n-1), where BM is the BinomialMean transform. BM is defined by (BM)a(n)=(M^n)a(0) where (M)a(n) is the mean (a(n)+a(n+1))/2, or, alternatively, by (BM)a(n)=Sum[C(n,k)a(k),k=0..n]/(2^n). |
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12
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| 1, 3, 17, 211, 5793, 339491, 41326513, 10282961907, 5181436229441, 5258784071302723, 10717167529963833681, 43779339268428732008723, 358114286723184561034838497, 5862685570087914880854259126371
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OFFSET
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0,2
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COMMENT
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The BinomialMean transform of this sequence is given in A075272.
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REFERENCES
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Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
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EXAMPLE
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Given that a(0)=1 and a(1)=3. Then (BM)a(2)=(1+2*3+a(2))/4=2a(1)=6, hence a(2)=17.
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MAPLE
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iBM:= proc(p) proc (n) option remember; add (2^(k) *p(k) *(-1)^(n-k) *binomial(n, k), k=0..n) end end: aa:='aa': a:= iBM(aa): aa:= n-> `if`(n=0, 1, 2*a(n-1)): seq (a(n), n=0..16); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 09 2008]
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CROSSREFS
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Sequence in context: A158885 A133991 A009494 this_sequence A072350 A084040 A009495
Adjacent sequences: A075268 A075269 A075270 this_sequence A075272 A075273 A075274
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KEYWORD
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eigen,nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Sep 11 2002
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 09 2008
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