%I #24 Aug 04 2024 06:36:59
%S 1,0,-3,-30,-63,12540,602877,6625710,-1991169183,-241970036520,
%T -7540177734243,2917041754949850,699983161534169697,
%U 46722975483964508820,-21334067257986056115363,-8882421213380429461235610,-1081286159351846822872767423
%N Expansion of e.g.f. sech(log(cos(x))) (even exponents only).
%F E.g.f.: sech(log(cos(x))) = 2*cos(x)/(1+cos^2(x)) is the reciprocal of the e.g.f. of A012007. - _Peter Bala_, Dec 02 2011
%e 1 - (3/4!)*x^4 - (30/6!)*x^6 - (63/8!)*x^8 + (12540/10!)*x^10 ...
%t With[{nn=40},Take[CoefficientList[Series[Sech[Log[Cos[x]]],{x,0,nn}], x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Dec 16 2011 *)
%Y Cf. A012003, A012007, A012008.
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E More terms from _Harvey P. Dale_, Dec 16 2011
%E New name from _Michel Marcus_, Aug 04 2024