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 A263187 G.f. B(x) satisfies: B( x - x*A(x) ) = x such that A( x - A(x)*B(x) ) = x, where A(x) is the g.f. of A263186. 1
 1, 1, 3, 14, 85, 615, 5038, 45265, 437012, 4472197, 48056889, 538621852, 6265669760, 75369364118, 934809950418, 11928201381716, 156302591148741, 2100191239445909, 28901831807930949, 406933300084065353, 5857010329019250612, 86111062850900773745, 1292373792900901543026, 19788451519046405896069 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..24. FORMULA G.f. B(x) and A(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.: 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 +... such that A(x - A(x)*B(x)) = x and B(x - x*A(x)) = x where 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 +... 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(B, n)} for(n=1, 30, print1(a(n), ", ")) CROSSREFS Cf. A263186. Sequence in context: A230218 A301934 A160881 * A213628 A088716 A005189 Adjacent sequences: A263184 A263185 A263186 * A263188 A263189 A263190 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 03 2015 STATUS approved

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Last modified June 5 19:06 EDT 2023. Contains 363138 sequences. (Running on oeis4.)