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 A195947 E.g.f. satisfies: A(x) = Sum_{n>=0} (-1)^n/n! * Sum_{k=0..n} (-1)^k*C(n,k)*(1 + x*A(x)^k)^k. 5
 1, 1, 5, 58, 1093, 28731, 971719, 40236449, 1972617385, 111779567596, 7189852342091, 517600784497237, 41237095369088029, 3602389000897583001, 342422738142493542031, 35186740743134660359186, 3887047020291801938191057, 459397561144034558519708403 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA E.g.f. satisfies: A(x) = Sum_{n>=0} A(x)^(n^2)*exp(A(x)^n - 1)*x^n/n!. EXAMPLE E.g.f.: A(x) = 1 + x + 5*x^2/2! + 58*x^3/3! + 1093*x^4/4! + 28731*x^5/5! +... where: A(x) = 1 + A(x)*exp(A(x) - 1)*x + A(x)^4*exp(A(x)^2 - 1)*x^2/2! + A(x)^9*exp(A(x)^3 - 1)*x^3/3! + A(x)^16*exp(A(x)^4 - 1)*x^4/4! +... Also, e.g.f. A = A(x) satisfies: A(x) = 1 - (1 - (1+x*A)) + 1/2!*(1 - 2*(1+x*A) + (1+x*A^2)^2) - 1/3!*(1 - 3*(1+x*A) + 3*(1+x*A^2)^2 - (1+x*A^3)^3) + 1/4!*(1 - 4*(1+x*A) + 6*(1+x*A^2)^2 - 4*(1+x*A^3)^3 + (1+x*A^4)^4) - 1/5!*(1 - 5*(1+x*A) + 10*(1+x*A^2)^2 - 10*(1+x*A^3)^3 + 5*(1+x*A^4)^4 - (1+x*A^5)^5) +-... PROG (PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); for(i=1, n, A=1+sum(m=1, n, exp(A^m-1)*A^(m^2)*X^m/m!)); n!*polcoeff(A, n)} (PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); for(i=1, n, A=1+sum(m=1, n, 1/m!*sum(k=0, m, binomial(m, k)*(-1)^(m-k)*(1+X*A^k)^k))); n!*polcoeff(A, n)} CROSSREFS Cf. A196022, A195895. Sequence in context: A151424 A097631 A130768 * A156326 A336258 A001624 Adjacent sequences:  A195944 A195945 A195946 * A195948 A195949 A195950 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 27 2011 STATUS approved

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Last modified June 25 09:38 EDT 2022. Contains 354835 sequences. (Running on oeis4.)