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A376098
Expansion of e.g.f. -LambertW(-2*x / (1 - x))/2.
2
0, 1, 6, 66, 1112, 25640, 753552, 26950000, 1136106624, 55167345792, 3032389917440, 186130732899584, 12619351769121792, 936591263680543744, 75527892444435486720, 6575887645386829301760, 614790327790529665138688, 61429094739085165675446272
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f. A(x) satisfies A(x) = x * (A(x) + exp(2*A(x))).
E.g.f.: Series_Reversion( x / (x + exp(2*x)) ).
a(n) = n! * Sum_{k=1..n} (2*k)^(k-1) * binomial(n-1,k-1)/k!.
a(n) = n * A352448(n-1).
a(n) ~ (2 + exp(-1))^(n + 1/2) * n^(n-1) / 2^(3/2). - Vaclav Kotesovec, Sep 10 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-2*x/(1-x))/2)))
(PARI) a(n) = n!*sum(k=1, n, (2*k)^(k-1)*binomial(n-1, k-1)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 10 2024
STATUS
approved