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%I #29 Jun 08 2023 08:51:41
%S 1,1,-1,-3,5,25,-61,-427,1385,12465,-50521,-555731,2702765,35135945,
%T -199360981,-2990414715,19391512145,329655706465,-2404879675441,
%U -45692713833379,370371188237525,7777794952988025,-69348874393137901,-1595024111042171723,15514534163557086905
%N Expansion of e.g.f.: (1+x)*sech(x).
%C Transform of binomial(1,n) under the matrix A119879.
%H Robert Israel, <a href="/A119882/b119882.txt">Table of n, a(n) for n = 0..480</a>
%F a(n) = Sum_{k=0..n} A119879(n,k)*C(1,k).
%F 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
%F a(n) = EulerE[n] + n*EulerE[n-1], n>0. - _Benedict W. J. Irwin_, May 30 2016
%p seq(`if`(n::odd, n*euler(n-1), euler(n)), n=0..24); # _Peter Luschny_, May 30 2016
%t Table[EulerE[n] + n*EulerE[n-1], {n,20}] (* _Benedict W. J. Irwin_, May 30 2016 *)
%o (PARI) Vec(serlaplace((1+x)/cosh(x + O(x^30)))) \\ _Andrew Howroyd_, Feb 27 2018
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( (1+x)/Cosh(x) ))); // _G. C. Greubel_, Jun 07 2023
%o (SageMath)
%o def A119882(n): return n*euler_number(n-1) if n%2==1 else euler_number(n)
%o [A119882(n) for n in range(41)] # _G. C. Greubel_, Jun 07 2023
%Y Cf. A119879, A122045.
%K easy,sign
%O 0,4
%A _Paul Barry_, May 26 2006
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