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Search: id:A112552
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| A112552 |
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A modified Chebyshev transform of the second kind. |
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+0
5
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| 1, 0, 1, -2, 0, 1, 0, -3, 0, 1, 3, 0, -4, 0, 1, 0, 6, 0, -5, 0, 1, -4, 0, 10, 0, -6, 0, 1, 0, -10, 0, 15, 0, -7, 0, 1, 5, 0, -20, 0, 21, 0, -8, 0, 1, 0, 15, 0, -35, 0, 28, 0, -9, 0, 1, -6, 0, 35, 0, -56, 0, 36, 0, -10, 0, 1, 0, -21, 0, 70, 0, -84, 0, 45, 0, -11, 0, 1, 7, 0, -56, 0, 126, 0, -120, 0, 55, 0, -12, 0, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are A112553. Inverse is A112554. Riordan array product (1/(1+x^2),x)(1/(1+x^2),x/(1+x^2)).
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FORMULA
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Riordan array (1/(1+x^2)^2, x/(1+x^2)); Number triangle T(n, k)=(-1)^(n-k)*sum{j=0..n, (1+(-1)^(n-j))(1+(-1)^(j-k))C((j+k)/2, k)/4}.
Unsigned triangle = A128174 * A149310, as infinite lower triangular matrices, with row sums A052952: (1, 1, 3, 4, 8, 12, 21, 33,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 28 2007
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EXAMPLE
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Triangle begins
1;
0,1;
-2,0,1;
0,-3,0,1;
3,0,-4,0,1;
0,6,0,-5,0,1;
-4,0,10,0,-6,0,1;
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CROSSREFS
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Cf. A128174, A049310, A052952.
Adjacent sequences: A112549 A112550 A112551 this_sequence A112553 A112554 A112555
Sequence in context: A108045 A143728 A127368 this_sequence A048154 A134511 A112554
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 13 2005
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