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A195134
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E.g.f. A(x) satisfies: A(x) = cosh(x*A(x)) + sin(x*A(x)).
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0
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1, 1, 3, 14, 93, 796, 8407, 105832, 1551865, 26033680, 492708491, 10400139232, 242507271061, 6195709678016, 172208913873375, 5175087678675584, 167222667351260145, 5781987852483789056, 213003988054590430099, 8328278686225469009408, 344418854322690984069581
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OFFSET
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0,3
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COMMENTS
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Compare e.g.f. to W(x) = LambertW(-x)/(-x) = Sum_{n>=0} (n+1)^(n-1)*x^n/n!, which satisfies: W(x) = cosh(x*W(x)) + sinh(x*W(x)).
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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E.g.f. A(x) satisfies: A( x/(cosh(x) + sin(x)) ) = cosh(x) + sin(x).
E.g.f.: A(x) = (1/x)*Series_Reversion( x/(cosh(x) + sin(x)) ).
a(n) = [x^n] (cosh(x) + sin(x))^(n+1)/(n+1), where [x^n] F(x) denotes the coefficient of x^n in F(x).
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 3*x^2/2! + 14*x^3/3! + 93*x^4/4! + 796*x^5/5! +...
where
cosh(x*A(x)) = 1 + x^2/2! + 6*x^3/3! + 49*x^4/4! + 480*x^5/5! + 5641*x^6/6! +...
sin(x*A(x)) = x + 2*x^2/2! + 8*x^3/3! + 44*x^4/4! + 316*x^5/5! + 2766*x^6/6! +...
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PROG
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(PARI) {a(n)=local(X=x+x*O(x^n)); n!*polcoeff(1/x*serreverse(x/((cosh(X) + sin(X)))), n)}
(PARI) {a(n)=local(X=x+x*O(x^(2*n))); n!*polcoeff((cosh(X)+sin(X))^(n+1)/(n+1), n)}
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CROSSREFS
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Sequence in context: A183611 A101220 A078456 * A089462 A088342 A074531
Adjacent sequences: A195131 A195132 A195133 * A195135 A195136 A195137
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Sep 09 2011
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STATUS
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approved
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