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 A245115 E.g.f. satisfies: A'(x) = (cos(x) + sin(x)*A(x)) / (cos(x)*A(x) - sin(x)). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 7 16:40 EST 2021. Contains 349581 sequences. (Running on oeis4.)