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 A362690 E.g.f. satisfies A(x) = exp(x^2 + x * A(x)). 3
 1, 1, 5, 28, 245, 2816, 40537, 702976, 14270153, 332102656, 8719631981, 255020847104, 8222803663549, 289815184113664, 11085650268060929, 457386463819595776, 20248713707077863953, 957435459515190345728, 48157934732749633188565 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Essentially the same as A138293. LINKS Table of n, a(n) for n=0..18. Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA E.g.f.: -LambertW(-x * exp(x^2)) / x = exp( x^2 - LambertW(-x*exp(x^2)) ). a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^(n-k-1) / (k! * (n-2*k)!). a(n) ~ sqrt(1 + LambertW(2*exp(-2))) * 2^((n+1)/2) * n^(n-1) / (exp(n) * LambertW(2*exp(-2))^((n+1)/2)). - Vaclav Kotesovec, Nov 10 2023 PROG (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2-lambertw(-x*exp(x^2))))) CROSSREFS Cf. A349562, A362691. Cf. A125500, A138293, A362736. Sequence in context: A000530 A121674 A306181 * A116977 A362636 A238981 Adjacent sequences: A362687 A362688 A362689 * A362691 A362692 A362693 KEYWORD nonn AUTHOR Seiichi Manyama, May 01 2023 STATUS approved

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Last modified May 28 18:29 EDT 2024. Contains 372919 sequences. (Running on oeis4.)