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Search: id:A131310
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| A131310 |
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O.g.f. A(x) satisfies: [x^n] exp(x*A(x)) = [x^n] A(x) / n!. |
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+0
1
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| 1, 1, 3, 25, 697, 87261, 63362851, 319794398533, 12896670350677905, 4680059818474453354777, 16983047870459137946598471811, 677909112049327323648624151866814641
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OFFSET
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0,3
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FORMULA
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a(n+1) = n!*Sum_{k=0..n} (k+1)/(n-k)!*a(k)*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 08 2008
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EXAMPLE
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O.g.f.: A(x) = 1 + x + 3*x^2 + 25*x^3 + 697*x^4 + 87261*x^5 + 63362851*x^6 +...
exp(x*A(x)) = 1 + x + 3*x^2/2! + 25*x^3/3! + 697*x^4/4! + 87261*x^5/5! + 63362851*x^6/6! +...
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PROGRAM
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(PARI) {a(n)=local(E=1+x+x*O(x^n), F); for(j=0, n, F=exp(x*E); E=sum(i=0, n, polcoeff(F, i)*i!*x^i)); polcoeff(E, n)}
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CROSSREFS
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Sequence in context: A009843 A136173 A003024 this_sequence A127231 A062411 A136516
Adjacent sequences: A131307 A131308 A131309 this_sequence A131311 A131312 A131313
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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), Jun 27 2007
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