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 A357009 E.g.f. satisfies log(A(x)) = (exp(x) - 1)^2 * A(x). 2
 1, 0, 2, 6, 50, 390, 4322, 53046, 782210, 12920550, 241747682, 5000171286, 113961184130, 2830240421190, 76196913418082, 2209152734071926, 68655746019566210, 2276606079902438310, 80244521295497399522, 2995966456305973559766, 118119901491333724203650 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..20. Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (k+1)^(k-1) * Stirling2(n,2*k)/k!. E.g.f.: A(x) = Sum_{k>=0} (k+1)^(k-1) * (exp(x) - 1)^(2*k) / k!. E.g.f.: A(x) = exp( -LambertW(-(exp(x) - 1)^2) ). E.g.f.: A(x) = -LambertW(-(exp(x) - 1)^2)/(exp(x) - 1)^2. PROG (PARI) a(n) = sum(k=0, n\2, (2*k)!*(k+1)^(k-1)*stirling(n, 2*k, 2)/k!); (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^(k-1)*(exp(x)-1)^(2*k)/k!))) (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-(exp(x)-1)^2)))) (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-lambertw(-(exp(x)-1)^2)/(exp(x)-1)^2)) CROSSREFS Cf. A052880, A357010. Cf. A052859, A357024. Sequence in context: A080310 A103990 A079835 * A177454 A357086 A052332 Adjacent sequences: A357006 A357007 A357008 * A357010 A357011 A357012 KEYWORD nonn AUTHOR Seiichi Manyama, Sep 09 2022 STATUS approved

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Last modified September 21 08:32 EDT 2023. Contains 365499 sequences. (Running on oeis4.)