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%I #15 Mar 15 2023 15:00:23
%S 1,0,1,6,41,340,3361,38682,508241,7506504,123108961,2219822990,
%T 43648348985,929502984540,21311829302401,523455901397730,
%U 13712375005949345,381621247702458640,11244620308691664961,349715433597469496982,11448372539225223596105,393503844330372123056100,14169282835811140260616801
%N Expansion of e.g.f. sec(x/(1 - x)).
%C Lah transform of the sequence 1, 0, 1, 0, 5, 0, 61, 0, 1385, ... (A000364 interspersed with zeros).
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F E.g.f.: sec(x/(1 - x)).
%F a(n) ~ 4 * n! * (Pi+2)^(n-1) / Pi^(n+1). - _Vaclav Kotesovec_, Jul 28 2018
%p a:=series(sec(x/(1 - x)), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # _Paolo P. Lava_, Mar 26 2019
%t nmax = 22; CoefficientList[Series[Sec[x/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
%t Table[Sum[Binomial[n - 1, k - 1] Abs[EulerE[k]] n!/k!, {k, 0, n}], {n, 0, 22}]
%o (PARI) x = 'x + O('x^30); Vec(serlaplace(1/cos(x/(1 - x)))) \\ _Michel Marcus_, Jul 28 2018
%Y Cf. A000364, A317409.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Jul 27 2018
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