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A273378 Expansion of sqrt( cosh(x) / cos(x) ) = Sum_{n>=0} a(n) * x^(2n) / (2n)!. 0
1, 1, 3, 31, 553, 18961, 874203, 62142991, 5423159953, 655008561121, 92608009666803, 16986382591132351, 3541042896979933753, 917218574919912685681, 264626392137250618729803, 91981994791776047627320111, 35093294931542583405745553953, 15761280495157673681620641704641, 7683715734173928801016321555135203, 4330739041520082271329522758307378271, 2626405828066727295503315986000018932553 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
All terms seem to be odd.
LINKS
EXAMPLE
E.g.f.: A(x) = 1 + x^2/2! + 3*x^4/4! + 31*x^6/6! + 553*x^8/8! + 18961*x^10/10! + 874203*x^12/12! + 62142991*x^14/14! + 5423159953*x^16/16! + 655008561121*x^18/18! +...
where A(x)^2 = cosh(x) / cos(x):
A(x)^2 = 1 + 2*x^2 + 12*x^4 + 152*x^6 + 3472*x^8 + 126752*x^10 + 6781632*x^12 + 500231552*x^14 +...+ A000795(n)*x^(2*n)/(2*n)! +...
PROG
(PARI) {a(n) = (2*n)! * polcoeff( sqrt( cosh(x + x*O(x^(2*n))) / cos(x + x*O(x^(2*n))) ) , 2*n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Cf. A000795.
Sequence in context: A121563 A360343 A261471 * A266487 A229258 A319896
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 21 2016
STATUS
approved

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Last modified February 24 05:54 EST 2024. Contains 370294 sequences. (Running on oeis4.)