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Search: id:A104018
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| A104018 |
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Expansion of (asinh(1/sinh(asinh(1)-sqrt(2)x))-asinh(1))/sqrt(2). |
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1
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| 0, 1, 2, 6, 28, 180, 1448, 13944, 156592, 2010000, 29026592, 465749856, 8220541888, 158283827520, 3301678947968, 74168218575744, 1785106271372032, 45828856887701760, 1250094695454351872
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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D. M. Y. Sommerville, The Elements of Non-Euclidean Geometry, Dover Publications, 1958, pp. 235,243. MR0100246 (20 #6679)
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FORMULA
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Series reversion of e.g.f. A(x) is -A(-x).
E.g.f. A(x)=y satisfies y' = sinh(asinh(1)+sqrt(2)*y).
E.g.f.: (asinh(1/sinh(asinh(1)-sqrt(2)x))-asinh(1))/sqrt(2).
With C=sqrt(2): 1/[cosh(Cx)-C*sinh(Cx)] = 1 + 2x + 6x^2/2! + 28x^3/3! + 180x^4/4! +... - Ralf Stephan, Mar 01 2005
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EXAMPLE
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E.g.f. = x + x^2 + x^3 + 7/6*x^4 + 3/2*x^5 + 181/90*x^6 + 83/30*x^7 + ...
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PROGRAM
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(PARI) {a(n)=if(n<2, n>0, n--; n!*polcoeff( 1/sum(k=0, n, (-x)^k/k!*2^((k+1)\2), x*O(x^n)), n))}
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CROSSREFS
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Sequence in context: A052809 A136631 A002435 this_sequence A100526 A084262 A084870
Adjacent sequences: A104015 A104016 A104017 this_sequence A104019 A104020 A104021
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Feb 28 2005
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