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Search: id:A108044
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| A108044 |
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Triangle read by rows: right half of Pascal's triangle (A007318) interspersed with 0's. |
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+0
5
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| 1, 0, 1, 2, 0, 1, 0, 3, 0, 1, 6, 0, 4, 0, 1, 0, 10, 0, 5, 0, 1, 20, 0, 15, 0, 6, 0, 1, 0, 35, 0, 21, 0, 7, 0, 1, 70, 0, 56, 0, 28, 0, 8, 0, 1, 0, 126, 0, 84, 0, 36, 0, 9, 0, 1, 252, 0, 210, 0, 120, 0, 45, 0, 10, 0, 1, 0, 462, 0, 330, 0, 165, 0, 55, 0, 11, 0, 1, 924, 0, 792, 0, 495, 0, 220, 0, 66
(list; table; graph; listen)
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OFFSET
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0,4
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REFERENCES
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L. W. Shapiro, S. Getu, W.-J. Woan and L. C. Woodson, The Riordan group, Discrete Applied Math., 34 (1991), 229-239.
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FORMULA
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Each entry is the sum of those in the previous row that are to its left and to its right.
Riordan array (1/sqrt(1-4*x^2), (1-sqrt(1-4*x^2))/(2*x)).
T(n, k)=binomial(n, (n+k)/2) if n+k is even, T(n, k)=0 if n+k is odd. G.f.=f/(1-tg), where f=1/sqrt(1-4x^2) and g=(1-sqrt(1-4x^2))/(2x). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 05 2005
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EXAMPLE
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Triangle begins:
1
0 1
2 0 1
0 3 0 1
6 0 4 0 1
0 10 0 5 0 1
20 0 15 0 6 0 1
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MAPLE
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T:=proc(n, k) if n+k mod 2 = 0 then binomial(n, (n+k)/2) else 0 fi end: for n from 0 to 13 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form (Deutsch)
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CROSSREFS
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Cf. A007318, A108045.
Adjacent sequences: A108041 A108042 A108043 this_sequence A108045 A108046 A108047
Sequence in context: A134511 A112554 A120616 this_sequence A104477 A052173 A124305
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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njas, Jun 02 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Christian G. Bower (bowerc(AT)usa.net), Jun 05 2005
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