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A361193
E.g.f. satisfies A(x) = exp( -2*x*A(x) ) / (1-x).
3
1, -1, 6, -50, 648, -10952, 232336, -5919664, 176435328, -6024464000, 231972167424, -9946181374208, 470038191434752, -24276240445152256, 1360508977539004416, -82233680186863536128, 5332689963474238341120, -369321737420738845638656
OFFSET
0,3
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,k)/k!.
E.g.f.: LambertW( 2*x/(1-x) ) / (2*x).
PROG
(PARI) a(n) = n!*sum(k=0, n, (-2)^k*(k+1)^(k-1)*binomial(n, k)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(lambertw(2*x/(1-x))/(2*x)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 03 2023
STATUS
approved