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 A126342 Denominators of the limit of coefficients of q in { [x^n] W(x,q) } when read backward from [q^(n*(n-1)/2)] to [q^(n*(n-1)/2 - (n-1))], where W satisfies: W(x,q) = exp( q*x*W(q*x,q) ). 3
 1, 2, 1, 6, 1, 1, 24, 3, 12, 3, 40, 2, 8, 8, 4, 720, 120, 240, 360, 120, 120, 840, 360, 72, 720, 120, 360, 720, 40320, 1680, 10080, 630, 4032, 5040, 672, 560, 72576, 840, 40320, 120960, 1920, 40320, 24192, 8064, 2520, 3628800, 362880, 145152, 4536, 725760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS When the fractions {A126341(k)/A126342(k), k>=1} are formatted as a triangle in which row n is then multiplied by n!, the result is integer triangle A126343. LINKS FORMULA A126341(n)/A126342(n) = A126265(n, n*(n-1)/2) / n! for n>=1. EXAMPLE The function W that satisfies: W(x,q) = exp( q*x*W(q*x,q) ) begins: W(x,q) = 1 + q*x + (1/2 + q)*q^2*x^2 + (1/6 + 1*q + 1/2*q^2 + 1*q^3)*q^3*x^3 + (1/24 + 1/2*q + 1*q^2 + 7/6*q^3 + 1*q^4 + 1/2*q^5 + 1*q^6)*q^4*x^4 +... Coefficients of q in {[x^n] W(x,q)} tend to a limit when read backwards: n=1: [1, 1/2]; n=2: [1, 1/2, 1, 1/6]; n=3: [1, 1/2, 1, 7/6, 1, 1/2, 1/24]. The limit of coefficients of q in { [x^n] W(x,q) } begins: [1, 1/2, 1, 7/6, 2, 2, 85/24, 11/3, 65/12, 19/3, 357/40, 19/2, 111/8, 123/8, 81/4, 16891/720,...]. PROG (PARI) {a(n)=local(W=1+x); for(i=0, n, W=exp(subst(x*W, x, q*x+O(x^(n+2))))); denominator(Vec(Vec(W)[n+2]+O(q^(n*(n+1)/2+2)))[n*(n-1)/2+1])} CROSSREFS Cf. A126341 (numerators), A126343, A126265. Sequence in context: A290318 A139547 A323855 * A229818 A324500 A082388 Adjacent sequences:  A126339 A126340 A126341 * A126343 A126344 A126345 KEYWORD frac,nonn AUTHOR Paul D. Hanna, Dec 25 2006 STATUS approved

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Last modified December 7 20:33 EST 2019. Contains 329849 sequences. (Running on oeis4.)