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 A155807 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n+1)). 3
 1, 1, 5, 55, 969, 23661, 741013, 28363707, 1284098609, 67149601273, 3984121444581, 264485848799679, 19426332734137849, 1564277403496216293, 137040382838351173301, 12977244383702330201731 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..15. FORMULA E.g.f. satisfies: A(x) = B(x*A(x)) and A(x/B(x)) = B(x) where B(x) satisfies: B(x) = Sum_{n>=0} x^n/n! * B(x)^(n^2) and is the e.g.f. of A155806. EXAMPLE E.g.f.: A(x) = 1 + x + 5*x^2/2! + 55*x^3/3! + 969*x^4/4! + 23661*x^5/5! +... where e.g.f. A(x) satisfies: A(x) = 1 + x*A(x)^2 + x^2/2!*A(x)^6 + x^3/3!*A(x)^12 + x^4/4!*A(x)^20 +... Let B(x) = A(x/B(x)) be the e.g.f. of A155806 then: B(x) = 1 + x*B(x) + x^2/2!*B(x)^4 + x^3/3!*B(x)^9 + x^4/4!*B(x)^16 +... B(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 269*x^4/4! + 4616*x^5/5! + 102847*x^6/6! +... PROG (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+sum(k=1, n, x^k*A^(k*(k+1))/k!+x*O(x^n))); n!*polcoeff(A, n)} CROSSREFS Cf. A155804, A155805, A155806. Sequence in context: A293013 A195513 A172493 * A135861 A141361 A203013 Adjacent sequences: A155804 A155805 A155806 * A155808 A155809 A155810 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 27 2009 STATUS approved

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Last modified June 22 07:39 EDT 2024. Contains 373565 sequences. (Running on oeis4.)