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 A372315 Expansion of e.g.f. exp( x - LambertW(-2*x)/2 ). 4
 1, 2, 8, 68, 960, 18832, 471136, 14324480, 512733696, 21119803136, 984029612544, 51169331031040, 2937675286583296, 184560174104465408, 12594824112085327872, 927757127285523243008, 73369903633161123397632, 6200198958236463387836416 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..17. Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA a(n) = Sum_{k=0..n} (2*k+1)^(k-1) * binomial(n,k). G.f.: Sum_{k>=0} (2*k+1)^(k-1) * x^k / (1-x)^(k+1). a(n) ~ 2^(n-1) * n^(n-1) * exp((exp(-1) + 1)/2). - Vaclav Kotesovec, May 04 2024 PROG (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-2*x)/2))) (PARI) a(n) = sum(k=0, n, (2*k+1)^(k-1)*binomial(n, k)); CROSSREFS Cf. A088957, A360193, A372316, A372320, A372321. Cf. A362694. Sequence in context: A361213 A156448 A262479 * A192550 A157752 A055547 Adjacent sequences: A372312 A372313 A372314 * A372316 A372317 A372318 KEYWORD nonn AUTHOR Seiichi Manyama, Apr 27 2024 STATUS approved

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Last modified June 22 07:39 EDT 2024. Contains 373565 sequences. (Running on oeis4.)