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A012009
Expansion of e.g.f. sech(log(cos(x))) (even exponents only).
1
1, 0, -3, -30, -63, 12540, 602877, 6625710, -1991169183, -241970036520, -7540177734243, 2917041754949850, 699983161534169697, 46722975483964508820, -21334067257986056115363, -8882421213380429461235610, -1081286159351846822872767423
OFFSET
0,3
FORMULA
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
EXAMPLE
1 - (3/4!)*x^4 - (30/6!)*x^6 - (63/8!)*x^8 + (12540/10!)*x^10 ...
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
EXTENSIONS
More terms from Harvey P. Dale, Dec 16 2011
New name from Michel Marcus, Aug 04 2024
STATUS
approved