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 A362735 E.g.f. satisfies A(x) = exp(x + x / A(x)^2). 4
 1, 2, -4, 56, -1008, 25632, -833600, 33067904, -1548418816, 83597525504, -5112566055936, 349330707068928, -26374805535322112, 2180554321981349888, -195926186031705505792, 19010400989418574020608, -1980997069982960384409600, 220651645970702249702326272 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..339 Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA E.g.f.: sqrt( 2*x / LambertW(2*x*exp(-2*x)) ) = exp( x + LambertW(2*x*exp(-2*x))/2 ). a(n) = Sum_{k=0..n} (-2*k+1)^(n-1) * binomial(n,k) = 2^n * A349720(n). PROG (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(2*x*exp(-2*x))/2))) CROSSREFS Cf. A349562, A362693, A362694, A362734. Cf. A349720. Sequence in context: A062784 A318642 A230884 * A185182 A098626 A012370 Adjacent sequences: A362732 A362733 A362734 * A362736 A362737 A362738 KEYWORD sign AUTHOR Seiichi Manyama, May 01 2023 STATUS approved

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Last modified September 11 13:11 EDT 2024. Contains 375829 sequences. (Running on oeis4.)