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 A219228 O.g.f. satisfies: A(x) = Sum_{n>=0} A(x)^n * (n^3*x)^n/n! * exp(-n^3*x*A(x)). 2
 1, 1, 32, 3119, 625710, 214333471, 112105268136, 83149960883200, 83014425998481126, 107334569041127441462, 174471878478682785998864, 348242875992753988109552778, 837327855535084109106340786272, 2387108242583316451939303856237037 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare to the o.g.f. of A217913: Sum_{n>=0} (n^3)^n*exp(-n^3*x)*x^n/n! = Sum_{n>=0} Stirling2(3*n,n)*x^n. LINKS FORMULA O.g.f. satisfies: A(x) = Sum_{n>=0} Stirling2(3*n,n) * x^n * A(x)^n. EXAMPLE O.g.f.: A(x) = 1 + x + 32*x^2 + 3119*x^3 + 625710*x^4 + 214333471*x^5 +... where A(x) = 1 + x*A(x)*exp(-x*A(x)) + 2^6*x^2*A(x)^2/2!*exp(-8*x*A(x)) + 3^9*x^3*A(x)^3/3!*exp(-27*x*A(x)) + 4^12*x^4*A(x)^4/4!*exp(-64*x*A(x)) + 5^15*x^5*A(x)^5/5!*exp(-125*x*A(x)) +... simplifies to a power series in x with integer coefficients. G.f. A(x) satisfies A(x) = G(x*A(x)) where G(x) = A(x/G(x)) begins: G(x) = 1 + x + 31*x^2 + 3025*x^3 + 611501*x^4 + 210766920*x^5 + 110687251039*x^6 +...+ Stirling2(3*n,n)*x^n +... PROG (PARI) {a(n)=local(A=1); for(i=1, n, A=sum(m=0, n, (m^3*x*A)^m/m!*exp(-m^3*x*A+x*O(x^n)))); polcoeff(A, n)} for(n=0, 21, print1(a(n), ", ")) CROSSREFS Cf. A217913, A219184, A217900, A218681, A218672. Sequence in context: A064018 A067321 A104652 * A135787 A016793 A215045 Adjacent sequences:  A219225 A219226 A219227 * A219229 A219230 A219231 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 15 2012 STATUS approved

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Last modified October 23 10:00 EDT 2019. Contains 328345 sequences. (Running on oeis4.)