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A227051 E.g.f.: 1/(cos(x) - sin(x)*sinh(x)), omitting the zero-valued coefficients of odd powers of x. 0
1, 3, 53, 2333, 191673, 25307913, 4900979093, 1308599657693, 460755584003313, 206844794964734673, 115313659955341400333, 78158334287649490486853, 63294640267864707577746153, 60357724113527363258814802233, 66943314938342593826952764256773, 85443499990582824984241143043808813 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(n) == 3 (mod 10) for n>0 (conjecture).

a(n) ~ 2*(2*n)! / ((sin(r)+cos(r)*sinh(r)+sin(r)*cosh(r)) * r^(2*n+1)), where r = 0.825607669071161851569946... is the root of the equation sin(r)*sinh(r) = cos(r). - Vaclav Kotesovec, Jul 13 2014

EXAMPLE

E.g.f.: A(x) = 1 + 3*x^2/2! + 53*x^4/4! + 2333*x^6/6! + 191673*x^8/8! + 25307913*x^10/10! +...

MATHEMATICA

Table[n!*SeriesCoefficient[1/(Cos[x] - Sin[x]*Sinh[x]), {x, 0, n}], {n, 0, 40, 2}] (* Vaclav Kotesovec, Jul 13 2014 *)

PROG

(PARI) {a(n)=local(X=x+x*O(x^(2*n))); (2*n)!*polcoeff(1/(cos(X) - sin(X)*sinh(X)), 2*n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A185071.

Sequence in context: A300420 A300683 A296678 * A300606 A301348 A296680

Adjacent sequences:  A227048 A227049 A227050 * A227052 A227053 A227054

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 29 2013

STATUS

approved

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Last modified December 8 05:15 EST 2021. Contains 349590 sequences. (Running on oeis4.)