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Search: id:A108666
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| A108666 |
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Number of (1,1)-steps in all Delannoy paths of length n (a Delannoy path of length n is a path from (0,0) to (n,n), consisting of steps E=(1,0), N=(0,1), and D=(1,1)). |
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+0
3
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| 0, 1, 8, 57, 384, 2505, 16008, 100849, 628736, 3888657, 23900040, 146146473, 889928064, 5399971161, 32668236552, 197123362785, 1186790473728, 7131032334369, 42773183020296, 256161548120857, 1531966218561920
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=sum(k*A104684(k),k=0..n)
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REFERENCES
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R. A. Sulanke, Objects counted by the central Delannoy numbers, J. of Integer Sequences, 6, 2003, Article 03.1.5.
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FORMULA
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a(n)=sum(k*binomial(n, k)*binomial(2n-k, n), k=1..n). G.f.=z(1-z)/(1-6z+z^2)^(3/2).
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EXAMPLE
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a(2)=8 because in the 13 (=A001850(2)) Delannoy paths of length 2, namely, DD, DNE,DEN,NED,END,NDE,EDN,NENE,NEEN,ENNE,ENEN,NNEE, and EENN, we have a total of eight D steps.
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MAPLE
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a:=n->sum(k*binomial(n, k)*binomial(2*n-k, n), k=1..n): seq(a(n), n=0..24);
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CROSSREFS
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Cf. A001850, A104684.
Adjacent sequences: A108663 A108664 A108665 this_sequence A108667 A108668 A108669
Sequence in context: A143570 A096711 A079926 this_sequence A023000 A097114 A022038
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 07 2005
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