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A012007
cosh(log(cos(x))) = 1+3/4!*x^4+30/6!*x^6+693/8!*x^8+25260/10!*x^10...
4
1, 0, 3, 30, 693, 25260, 1351383, 99680490, 9695756073, 1202439837720, 185185594118763, 34674437196568950, 7757267081778543453, 2043536254646561946180, 626129820701814932734143, 220771946624511552276841410, 88759695789769644718332394833
OFFSET
0,3
FORMULA
a(n) = (1/2)*((-1)^n+A000364(n)). Also cosh(log(cos(x))) = 1/2*(cos(x)+1/cos(x)) is the reciprocal of the e.g.f. of A012009. - Peter Bala, Dec 02 2011
MATHEMATICA
terms = 15; s = Cosh[Log[Cos[x]]] + O[x]^(2*terms); CoefficientList[s, x^2] * Table[(2n)!, {n, 0, terms-1}] (* Jean-François Alcover, May 22 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
EXTENSIONS
Confirmed by N. J. A. Sloane, Dec 17 2011
STATUS
approved