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Search: id:A136727
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| A136727 |
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E.g.f.: A(x) = [ exp(x)/(3 - 2*exp(x)) ]^(1/3). |
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+0
4
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| 1, 1, 3, 17, 139, 1481, 19443, 303297, 5480219, 112549881, 2589274883, 65957355377, 1842897053099, 56038776055081, 1842278768795923, 65109900167188257, 2461735422517374779, 99148196540813749081
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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G.f. of variant A014307 is B(x) = sqrt(exp(x)/(2-exp(x))), which satisfies: B(x) = 1 + integral(B(x)^3*exp(-x)).
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FORMULA
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E.g.f. A(x) satisfies: A(x) = 1 + integral( A(x)^4 * exp(-x) ).
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 3/2*x^2 + 17/6*x^3 + 139/24*x^4 + 1481/120*x^5 +...
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PROGRAM
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(PARI) {a(n)=n!*polcoeff((exp(x +x*O(x^n))/(3-2*exp(x +x*O(x^n))))^(1/3), n)} (PARI) /* As solution to integral equation: */ {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+intformal(A^4*exp(-x+x*O(x^n)))); n!*polcoeff(A, n)} for(n=0, 41, print1(a(n), ", "))
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CROSSREFS
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Cf. variants: A014307, A136728, A136729.
Adjacent sequences: A136724 A136725 A136726 this_sequence A136728 A136729 A136730
Sequence in context: A006290 A060003 A025167 this_sequence A120022 A001865 A087885
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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