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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
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. A362694.
Sequence in context: A361213 A156448 A262479 * A192550 A157752 A055547
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.)