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 A307103 G.f. A(x) satisfies x = A( A(x) + 4*A(x)^2 ). 0
 0, 1, -2, 12, -96, 880, -8720, 90752, -975936, 10737152, -120093056, 1360051456, -15556087296, 179424700416, -2084953411584, 24393551634432, -287204585508864, 3400978267127808, -40480500900446208, 484006813958356992, -5810240353159839744, 70001749695581061120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = -(-1)^n * A213422(n). Composition inverse of A027436. EXAMPLE G.f. = x - 2*x^2 + 12*x^3 - 96*x^4 + 880*x^5 - 8720*x^6 + 90752*x^7 + ... MATHEMATICA a[ n_] := Module[ {A, x}, A = x; Do[ A += x O[x]^k; A = Normal[A] + x^k ((-4)^(k-1) CatalanNumber[k-1] - SeriesCoefficient[ ComposeSeries[A, A], k])/2, {k, 2, n}]; oefficient[A, x, n]]; PROG (PARI) {a(n) = my(A); A = x; for(k=2, n, A += x*O(x^k); A = truncate(A) + x^k * ((-4)^(k-1) * binomial(2*k-2, k-1)/k - polcoeff(subst(A, x, A), k))/2); polcoeff(A, n)}; CROSSREFS Cf. A027436, A213422. Sequence in context: A292419 A322543 A213422 * A153231 A052564 A014297 Adjacent sequences:  A307100 A307101 A307102 * A307104 A307105 A307106 KEYWORD sign AUTHOR Michael Somos, Mar 24 2019 STATUS approved

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Last modified October 23 14:43 EDT 2019. Contains 328345 sequences. (Running on oeis4.)