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 A192949 E.g.f. satisfies: A(x) = 1 + x*Sum_{n>=0} (A(x)^2 - 1)^n/n!. 1
 1, 1, 4, 42, 704, 16300, 482112, 17366776, 737738752, 36109329552, 2001104000000, 123856655495584, 8468525621182464, 633915692700252352, 51562270240172425216, 4528439794201950000000, 427082984690083973562368, 43049504748861000404766976 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA E.g.f. A(x) equals the formal inverse of function (x-1)/exp(x^2-1). E.g.f. satisfies: A(x) = 1 + x*exp(A(x)^2-1). E.g.f.: A(x) = 1 + Series_Reversion( x/exp(2*x + x^2) ). E.g.f. satisfies: A(x/G(x)) = 1 + x where G(x) = exp(2*x+x^2) = x/Series_Reversion(A(x)-1) = e.g.f. of A000898. EXAMPLE E.g.f.: A(x) = 1 + x + 4*x^2/2! + 42*x^3/3! + 704*x^4/4! + 16300*x^5/5! +... where (A(x) - 1)/exp(A(x)^2-1) = x. Related expansions. (A(x)^2-1) = 2*x + 10*x^2/2! + 108*x^3/3! + 1840*x^4/4! + 43000*x^5/5! +... (A(x)^2-1)^2 = 8*x^2/2! + 120*x^3/3! + 2328*x^4/4! + 58400*x^5/5! +... (A(x)^2-1)^3 = 48*x^3/3! + 1440*x^4/4! + 43920*x^5/5! +... (A(x)^2-1)^4 = 384*x^4/4! + 19200*x^5/5! + 846720*x^6/6! +... PROG (PARI) {a(n)=local(A=1+serreverse(x/exp(2*x+x^2+x^2*O(x^n)))); n!*polcoeff(A, n)} (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*exp(A^2-1+x*O(x^n))); n!*polcoeff(A, n)} (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*sum(m=0, n, (A^2-1+x*O(x^n))^m/m!)); n!*polcoeff(A, n)} CROSSREFS Cf. A192945, A192667, A000898, A000169. Sequence in context: A216080 A137645 A136045 * A156453 A074768 A140055 Adjacent sequences:  A192946 A192947 A192948 * A192950 A192951 A192952 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 13 2011 STATUS approved

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Last modified May 23 16:49 EDT 2013. Contains 225610 sequences.