A365036 - OEIS

A365036

E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^2)).

1, 1, 3, -5, -23, 521, -1829, -71021, 1319697, 5905297, -683965709, 8664974891, 311864420473, -13981842414695, 6694007756619, 16448800124183491, -448649039951220959, -13236887251789967071, 1210629233913421852387, -12065049302884271631269

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Lambert W-Function.

FORMULA

E.g.f.: exp( x + LambertW(2*x^2*exp(-2*x))/2 ).

a(n) = n! * Sum_{k=0..n} (-2*n+2*k+1)^(k-1) * binomial(k,n-k)/k!.

PROG

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(2*x^2*exp(-2*x))/2)))

CROSSREFS

Cf. A125500, A143768, A363354, A363529, A365035, A365037.

Cf. A361091.

Sequence in context: A137086 A137087 A214589 * A309844 A062218 A050280

Adjacent sequences: A365033 A365034 A365035 * A365037 A365038 A365039

KEYWORD

sign

AUTHOR

Seiichi Manyama, Aug 17 2023

STATUS

approved