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E.g.f. sech(log(x+1)/exp(x)).
1

%I #16 Nov 19 2016 03:09:16

%S 1,0,-1,9,-54,210,510,-24500,355544,-3310776,7970880,511460048,

%T -14772993312,247420878848,-2080751146656,-34093875419760,

%U 2085552636479488,-56037789835944320,880848150693672192

%N E.g.f. sech(log(x+1)/exp(x)).

%H G. C. Greubel, <a href="/A013567/b013567.txt">Table of n, a(n) for n = 0..400</a>

%e sech(log(x+1)/exp(x)) = 1 - 1/2!*x^2 + 9/3!*x^3 - 54/4!*x^4 + 210/5!*x^5 - ...

%t With[{nn=20},CoefficientList[Series[Sech[Log[x+1]/Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 09 2015 *)

%o (PARI) x='x+O('x^33); Vec(serlaplace(1/cosh(log(1+x)*exp(-x)))) \\ _Joerg Arndt_, Nov 17 2016

%K sign

%O 0,4

%A Patrick Demichel (patrick.demichel(AT)hp.com), Dec 11 1996