A365035 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x))).

1, 1, 3, 1, -11, 61, 301, -6299, 7561, 903673, -9019079, -145636919, 4305630781, 7516191541, -2037845181371, 22442805921901, 944219385367441, -29922880660473359, -288352494154313999, 32071808922904896913, -273044292430852251899

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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

Formula

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

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(x^2*exp(-x)))))

Crossrefs

Cf. A125500, A143768, A363354, A363529, A365036, A365037.

Cf. A361090.

Sequence in context: A002185 A002589 A048522 * A232460 A337205 A287197

Adjacent sequences: A365032 A365033 A365034 * A365036 A365037 A365038

Keyword

sign

Author

Seiichi Manyama, Aug 17 2023

Status

approved