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 A356795 E.g.f. satisfies A(x) = 1/(1 - x)^(x * A(x)^2). 3
 1, 0, 2, 3, 68, 330, 7674, 73080, 1883440, 28281960, 818625960, 17120406600, 557507325000, 15014517495120, 548643259812816, 18056683281775320, 736892260092195840, 28579282973977498560, 1295028345251832359616, 57666859088090317591680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA a(n) = n! * Sum_{k=0..floor(n/2)} (2*k+1)^(k-1) * |Stirling1(n-k,k)|/(n-k)!. E.g.f.: A(x) = Sum_{k>=0} (2*k+1)^(k-1) * (-x * log(1-x))^k / k!. E.g.f.: A(x) = exp( -LambertW(2 * x * log(1-x))/2 ). E.g.f.: A(x) = ( LambertW(2 * x * log(1-x))/(2 * x * log(1-x)) )^(1/2). PROG (PARI) a(n) = n!*sum(k=0, n\2, (2*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!); (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (2*k+1)^(k-1)*(-x*log(1-x))^k/k!))) (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(2*x*log(1-x))/2))) (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(2*x*log(1-x))/(2*x*log(1-x)))^(1/2))) CROSSREFS Cf. A066166, A355842, A356796. Cf. A356786. Sequence in context: A108023 A352163 A041249 * A360817 A184949 A132598 Adjacent sequences: A356792 A356793 A356794 * A356796 A356797 A356798 KEYWORD nonn AUTHOR Seiichi Manyama, Aug 28 2022 STATUS approved

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Last modified March 25 08:54 EDT 2023. Contains 361520 sequences. (Running on oeis4.)