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A136728
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E.g.f.: A(x) = [ exp(x)/(4 - 3*exp(x)) ]^(1/4).
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4
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1, 1, 4, 31, 349, 5146, 93799, 2036161, 51283894, 1470035101, 47250248569, 1683031711516, 65800765032589, 2801364476781781, 129003301751229364, 6389120632590635971, 338644807090096148809, 19126604338708282552186
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| E.g.f. A(x) satisfies: A(x) = 1 + integral( A(x)^5 * exp(-x) ).
O.g.f.: 1/(1 - x/(1-3*x/(1 - 5*x/(1-6*x/(1 - 9*x/(1-9*x/(1 - 13*x/(1-12*x/(1 - 17*x/(1-15*x/(1 - ...)))))))))), a continued fraction.
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PROG
| (PARI) {a(n)=n!*polcoeff((exp(x +x*O(x^n))/(4-3*exp(x +x*O(x^n))))^(1/4), 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)}
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CROSSREFS
| Cf. A201354, variants: A014307, A136727, A136729.
Sequence in context: A107725 A145160 A129271 * A102757 A145561 A201628
Adjacent sequences: A136725 A136726 A136727 * A136729 A136730 A136731
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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