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%I #14 Jun 05 2021 11:37:01
%S 0,1,0,0,4,-12,72,-168,544,8144,-91520,1384768,-11984128,149032128,
%T -1158162432,16299168896,-125837340672,2859883876608,-32260942757888,
%U 1008997773326336,-15535095938220032,466978134769624064
%N E.g.f.: log(sec(x) + arcsin(x)).
%H Matthew House, <a href="/A013195/b013195.txt">Table of n, a(n) for n = 0..449</a>
%e G.f. = x + 4*x^4 - 12*x^5 + 72*x^6 - 168*x^7 + 544*x^8 + 8144*x^9 - 91520*x^10 + ...
%t With[{nn=30},CoefficientList[Series[Log[Sec[x]+ArcSin[x]],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Jun 05 2021 *)
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); n! * polcoeff( log( 1 / cos(x + A) + asin(x + A) ), n))}; /* _Michael Somos_, Feb 17 2017 */
%K sign
%O 0,5
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E a(0) corrected by _Matthew House_, Feb 16 2017
%E New name from _Michael Somos_, Feb 16 2017
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