A245115 E.g.f. satisfies: A'(x) = (cos(x) + sin(x)*A(x)) / (cos(x)*A(x) - sin(x)).

1, 1, 1, 1, 3, 7, 25, 117, 567, 2931, 20165, 140169, 1008691, 8756711, 80546609, 736667037, 7767188015, 87947663355, 983717687645, 12138623741969, 162832820098219, 2156307692882095, 30489019112863689, 470349294170629989, 7212155129160617511, 114968617914648215939

Offset

0,5

Comments

Note that a(88) is negative. - Vaclav Kotesovec, Jul 29 2014

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Formula

E.g.f. satisfies:

(1) A(x) = (cos(x) + sin(x)*A'(x)) / (cos(x)*A'(x) - sin(x)).

(2) A(x) = 1 + Integral (cos(x) + sin(x)*A(x)) / (cos(x)*A(x) - sin(x)) dx.

Example

E.g.f.: A(x) = 1 + x + x^2/2! + x^3/3! + 3*x^4/4! + 7*x^5/5! + 25*x^6/6! +...

Prog

(PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); for(i=1, n, A=1+intformal((cos(X)+sin(X)*A)/(cos(X)*A-sin(X)+x*O(x^n)))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A054092 A096648 A156100 * A215772 A019056 A065163

Adjacent sequences: A245112 A245113 A245114 * A245116 A245117 A245118

Keyword

sign

Author

Paul D. Hanna, Jul 29 2014

Status

approved