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A375876
E.g.f. satisfies A(x) = exp( 2 * (exp(x) - 1) * A(x)^(1/2) ).
1
1, 2, 10, 76, 790, 10494, 170396, 3278174, 73019522, 1850066136, 52577005426, 1657084522790, 57382017574920, 2166149552961970, 88550946187572482, 3897682631534087692, 183810990395243463198, 9246950189455617225622, 494332095588897164709644
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052880.
E.g.f.: exp( - 2*LambertW(1 - exp(x)) ).
a(n) = 2 * Sum_{k=0..n} (k+2)^(k-1) * Stirling2(n,k).
a(n) ~ 2*sqrt(exp(1) + 1) * n^(n-1) / (exp(n-2) * (log(exp(1) + 1)-1)^(n - 1/2)). - Vaclav Kotesovec, Sep 06 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-2*lambertw(1-exp(x)))))
(PARI) a(n) = 2*sum(k=0, n, (k+2)^(k-1)*stirling(n, k, 2));
CROSSREFS
Sequence in context: A195136 A294573 A301741 * A140763 A245307 A292632
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 01 2024
STATUS
approved