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%I #10 Sep 08 2022 08:44:38
%S 1,0,1,3,16,70,580,3850,39940,350544,4408460,48605788,715662176,
%T 9518173080,160469679136,2503106438040,47524013744272,851125166412928,
%U 17967763294589776,363412179220061872
%N Expansion of e.g.f. sec(exp(x)*log(x+1)).
%H G. C. Greubel, <a href="/A012279/b012279.txt">Table of n, a(n) for n = 0..441</a>
%e E.g.f. = 1 + x^2/2! + 3*x^3/3! + 16*x^4/4! + 70*x^5/5! + ...
%p seq(coeff(series(factorial(n)*sec(exp(x)*log(x+1)),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 28 2018
%t With[{nn = 30}, CoefficientList[Series[Sec[Exp[x]*Log[x+1]], {x, 0, nn}], x] Range[0, nn]!] (* _G. C. Greubel_, Oct 28 2018 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(1/cos(exp(x)*log(x+1)))) \\ _G. C. Greubel_, Oct 28 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/Cos(Exp(x)*Log(x+1)) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // _G. C. Greubel_, Oct 28 2018
%K nonn
%O 0,4
%A Patrick Demichel (patrick.demichel(AT)hp.com)