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A155761
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Riordan array (c(2x^2),xc(2x^2)) where c(x) is the g.f. of A000108.
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2
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1, 0, 1, 2, 0, 1, 0, 4, 0, 1, 8, 0, 6, 0, 1, 0, 20, 0, 8, 0, 1, 40, 0, 36, 0, 10, 0, 1, 0, 112, 0, 56, 0, 12, 0, 1, 224, 0, 224, 0, 80, 0, 14, 0, 1, 0, 672, 0, 384, 0, 108, 0, 16, 0, 1, 1344, 0, 1440, 0, 600, 0, 140, 0, 18, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Inverse of Riordan array (1/(1+2x^2),x/(1+2x^2)). Row sums are A126087.
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FORMULA
| Triangle T(n,k)=((k+1)/(n+k+1))*C(n,(n-k)/2)*(1+(-1)^(n-k))*2^((n-k)/2).
T(n,k)=A053121(n,k)*2^((n-k)/2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 11 2009]
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EXAMPLE
| Triangle begins
1,
0, 1,
2, 0, 1,
0, 4, 0, 1,
8, 0, 6, 0, 1,
0, 20, 0, 8, 0, 1,
40, 0, 36, 0, 10, 0, 1,
0, 112, 0, 56, 0, 12, 0, 1,
224, 0, 224, 0, 80, 0, 14, 0, 1
Production matrix is
0, 1,
2, 0, 1,
0, 2, 0, 1,
0, 0, 2, 0, 1,
0, 0, 0, 2, 0, 1,
0, 0, 0, 0, 2, 0, 1,
0, 0, 0, 0, 0, 2, 0, 1,
0, 0, 0, 0, 0, 0, 2, 0, 1,
0, 0, 0, 0, 0, 0, 0, 2, 0, 1
0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1
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CROSSREFS
| Sequence in context: A111959 A110109 A145973 * A067631 A123641 A134317
Adjacent sequences: A155758 A155759 A155760 * A155762 A155763 A155764
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 26 2009
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