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 A213010 G.f. satisfies: A(x) = x+x^2 + x*A(A(x)). 5
 1, 2, 4, 16, 80, 480, 3296, 25152, 209600, 1884160, 18110080, 184898304, 1994964736, 22654449664, 269855506944, 3362350046208, 43715434232832, 591812683833344, 8326660788725760, 121550217508892672, 1838089917983911936, 28753297176215257088, 464675647688625364992 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The half-iteration of the g.f. equals an integer series (A213009). LINKS Paul D. Hanna, Table of n, a(n) for n = 1..256 FORMULA G.f. satisfies: A(x) = x/G(x) - 1 - G(x) where A(G(x)) = x. EXAMPLE G.f.: A(x) = x + 2*x^2 + 4*x^3 + 16*x^4 + 80*x^5 + 480*x^6 + 3296*x^7 +... where A(A(x)) = x + 4*x^2 + 16*x^3 + 80*x^4 + 480*x^5 + 3296*x^6 +... Related expansions. Let B(B(x)) = A(x), then B(x) is an integer series: B(x) = x + x^2 + x^3 + 5*x^4 + 21*x^5 + 125*x^6 + 825*x^7 + 6133*x^8 +... where the coefficients of B(x) are congruent to 1 modulo 4. PROG (PARI) {a(n)=local(A=x+2*x^2); for(i=1, n, A=x+x^2+x*subst(A, x, A+x*O(x^n))); polcoeff(A, n)} for(n=1, 31, print1(a(n), ", ")) CROSSREFS Cf. A213009, A030266, A215114, A215116, A215118. Sequence in context: A025225 A115125 A326859 * A000831 A000090 A295922 Adjacent sequences: A213007 A213008 A213009 * A213011 A213012 A213013 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 01 2012 STATUS approved

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Last modified February 5 23:07 EST 2023. Contains 360091 sequences. (Running on oeis4.)