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A119879
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Exponential Riordan array (sech(x),x).
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7
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1, 0, 1, -1, 0, 1, 0, -3, 0, 1, 5, 0, -6, 0, 1, 0, 25, 0, -10, 0, 1, -61, 0, 75, 0, -15, 0, 1, 0, -427, 0, 175, 0, -21, 0, 1, 1385, 0, -1708, 0, 350, 0, -28, 0, 1, 0, 12465, 0, -5124, 0, 630, 0, -36, 0, 1, -50521, 0, 62325, 0, -12810, 0, 1050, 0, -45, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Row sums have e.g.f. exp(x)*sech(x) (signed version of A009006). Inverse of masked Pascal triangle A119467. Transforms the sequence with e.g.f. g(x) to the sequence with e.g.f. g(x)*sech(x).
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FORMULA
| Number triangle whose k-th column has e.g.f. sech(x)*x^k/k!
T(n,k) = C(n,k)*2^(n-k)*E_{n-k}(1/2) where C(n,k) is the binomial coefficient and E_{m}(x) are the Euler polynomials. [From Peter Luschny (peter(AT)luschny.de), Jan 25 2009]
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EXAMPLE
| Triangle begins
1,
0, 1,
-1, 0, 1,
0, -3, 0, 1,
5, 0, -6, 0, 1,
0, 25, 0, -10, 0, 1,
-61, 0, 75, 0, -15, 0, 1,
0, -427, 0, 175, 0, -21, 0, 1,
1385, 0, -1708, 0, 350, 0, -28, 0, 1
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MAPLE
| T := (n, k) -> binomial(n, k)*2^(n-k)*euler(n-k, 1/2): [From Peter Luschny (peter(AT)luschny.de), Jan 25 2009]
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CROSSREFS
| Row sums are A155585. [From Johannes W. Meijer, Apr 20 2011]
Sequence in context: A079520 A191532 A179552 * A115714 A020768 A104544
Adjacent sequences: A119876 A119877 A119878 * A119880 A119881 A119882
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 26 2006
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