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Search: id:A143019
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| A143019 |
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Infinite square array read by antidiagonals: a(q,n)=is the coefficient of z^n in the series expansion of C(z)^q/(1-4z)^(3/2), where C(z)=[1-sqrt(1-4z)]/(2z) is the Catalan function (q,n=0,1,2,...). |
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1
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| 1, 1, 6, 1, 7, 30, 1, 8, 38, 140, 1, 9, 47, 187, 630, 1, 10, 57, 244, 874, 2772, 1, 11, 68, 312, 1186, 3958, 12012, 1, 12, 80, 392, 1578, 5536, 17548, 51480, 1, 13, 93, 485, 2063, 7599, 25147, 76627, 218790, 1, 14, 107, 592, 2655, 10254, 35401, 112028, 330818
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(q,n)=a(q-1,n)+a(q+1,n-1).
Row 0 is A002457; row 1 is A000531; row 2 is A029760; row 3 is A045720.
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FORMULA
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a(q,n)=Sum(4^i*binom(2n-2i+q,n-i), i=0..n).
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EXAMPLE
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Array starts:
1 6 30 140 630 ...
1 7 38 187 874 ...
1 8 47 244 1186 ...
1 9 57 312 1578 ...
.......
.......
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MAPLE
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a:=proc(q, n) options operator, arrow: sum(4^i*binomial(2*n-2*i+q, n-i), i= 0.. n) end proc: aa:=proc(q, n) options operator, arrow: a(q-1, n-1) end proc: matrix(10, 10, aa); # yields sequence in matrix form
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CROSSREFS
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Cf. A002457, A000531, A029760, A045720.
Sequence in context: A110942 A082830 A046902 this_sequence A156921 A094214 A001622
Adjacent sequences: A143016 A143017 A143018 this_sequence A143020 A143021 A143022
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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 24 2008
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