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 A263186 G.f. A(x) satisfies: A( x - A(x)*B(x) ) = x such that B( x - x*A(x) ) = x, where B(x) is the g.f. of A263187. 1
 1, 1, 4, 23, 160, 1260, 10861, 100474, 984944, 10142888, 109039530, 1218011097, 14086708075, 168205533546, 2069043383080, 26170130114863, 339856785957307, 4525776548471074, 61735297113781725, 861823700018556599, 12302696382913051859, 179461986070686773966, 2673380518707453159859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA G.f. A(x) and B(x) satisfy the differential series: (1) A(x) = x + Sum_{n>=1} d^(n-1)/dx^(n-1) A(x)^n * B(x)^n / n!. (2) B(x) = x + Sum_{n>=1} d^(n-1)/dx^(n-1) x^n * A(x)^n / n!. (3) A(x) = x * exp( Sum_{n>=1} d^(n-1)/dx^(n-1) A(x)^n * B(x)^n / (n!*x) ). (4) B(x) = x * exp( Sum_{n>=1} d^(n-1)/dx^(n-1) x^(n-1) * A(x)^n / n! ). EXAMPLE G.f.: A(x) = x + x^2 + 4*x^3 + 23*x^4 + 160*x^5 + 1260*x^6 + 10861*x^7 + 100474*x^8 + 984944*x^9 + 10142888*x^10 + 109039530*x^11 +... such that A(x - A(x)*B(x)) = x and B(x - x*A(x)) = x where B(x) = x + x^2 + 3*x^3 + 14*x^4 + 85*x^5 + 615*x^6 + 5038*x^7 + 45265*x^8 + 437012*x^9 + 4472197*x^10 + 48056889*x^11 +... PROG (PARI) {a(n) = my(A=x, B=x); for(i=1, n, A = serreverse(x - A*B +x*O(x^n)); B=serreverse(x - x*A); ); polcoeff(A, n)} for(n=1, 30, print1(a(n), ", ")) CROSSREFS Cf. A263187. Sequence in context: A326350 A198916 A182969 * A245110 A342988 A304074 Adjacent sequences:  A263183 A263184 A263185 * A263187 A263188 A263189 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 03 2015 STATUS approved

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Last modified June 23 07:38 EDT 2021. Contains 345395 sequences. (Running on oeis4.)