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A360939
E.g.f. satisfies A(x) = exp( 2*x*A(x) / (1-x) ).
2
1, 2, 16, 212, 4016, 99952, 3096448, 115063328, 4993598464, 248071645952, 13888585800704, 865481914527232, 59426130052458496, 4458258196636276736, 362864617248019800064, 31848507841521274769408, 2998685833332127139299328, 301504120063370711801724928
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * Sum_{k=0..n} 2^k * (k+1)^(k-1) * binomial(n-1,n-k)/k!.
E.g.f.: exp ( -LambertW(-2*x/(1-x)) ).
E.g.f.: -(1-x)/(2*x) * LambertW(-2*x/(1-x)).
a(n) ~ (1 + 2*exp(1))^(n + 1/2) * n^(n-1) / (sqrt(2) * exp(n - 1/2)). - Vaclav Kotesovec, Nov 10 2023
PROG
(PARI) a(n) = n!*sum(k=0, n, 2^k*(k+1)^(k-1)*binomial(n-1, n-k)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x/(1-x)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-(1-x)/(2*x)*lambertw(-2*x/(1-x))))
CROSSREFS
Cf. A361065.
Sequence in context: A349313 A364399 A365568 * A114531 A365585 A012056
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 04 2023
STATUS
approved