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 A131310 O.g.f. A(x) satisfies: [x^n] exp(x*A(x)) = [x^n] A(x) / n!. 0
 1, 1, 3, 25, 697, 87261, 63362851, 319794398533, 12896670350677905, 4680059818474453354777, 16983047870459137946598471811, 677909112049327323648624151866814641 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n+1) = n!*Sum_{k=0..n} (k+1)/(n-k)!*a(k)*a(n-k). - Vladeta Jovovic, Jul 08 2008 EXAMPLE 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! +... PROG (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)} CROSSREFS Sequence in context: A179473 A248417 A306795 * A127231 A062411 A136516 Adjacent sequences:  A131307 A131308 A131309 * A131311 A131312 A131313 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 27 2007 STATUS approved

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)