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A119882
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Expansion of e.g.f.: (1+x)*sech(x).
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1
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1, 1, -1, -3, 5, 25, -61, -427, 1385, 12465, -50521, -555731, 2702765, 35135945, -199360981, -2990414715, 19391512145, 329655706465, -2404879675441, -45692713833379, 370371188237525, 7777794952988025, -69348874393137901, -1595024111042171723, 15514534163557086905
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OFFSET
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0,4
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COMMENTS
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Transform of binomial(1,n) under the matrix A119879.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} A119879(n,k)*C(1,k).
E.g.f.: (1+x)/sech(x) = (1+x)*(1 - x^2/Q(0)), where Q(k) = (2*k+1)*(2*k+2) + x^2 - (2*k+1)*(2*k+2)*x^2/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 06 2013
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MAPLE
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seq(`if`(n::odd, n*euler(n-1), euler(n)), n=0..24); # Peter Luschny, May 30 2016
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MATHEMATICA
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PROG
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(PARI) Vec(serlaplace((1+x)/cosh(x + O(x^30)))) \\ Andrew Howroyd, Feb 27 2018
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( (1+x)/Cosh(x) ))); // G. C. Greubel, Jun 07 2023
(SageMath)
def A119882(n): return n*euler_number(n-1) if n%2==1 else euler_number(n)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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