A334316 E.g.f. A(x) satisfies: A(x) = x * exp(A(x)) * (1 - A(x)).

1, 0, -3, -8, 45, 576, 385, -54144, -499527, 4787200, 160740261, 558627840, -45943496027, -854266871808, 8403892043625, 590895130771456, 4982009666876145, -320936968832679936, -10133752613818727987, 75595253378088960000, 11587542472638176520861

Offset: 1

Author

Ilya Gutkovskiy, Apr 22 2020

Keywords

• sign

Comments

Exponential reversion of A000240 (rencontres numbers).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..400
• Index entries for reversions of series

Crossrefs

Cf. A000240, A052885.

Programs

Mathematica

nmax = 21; CoefficientList[InverseSeries[Series[x Exp[-x]/(1 - x), {x, 0, nmax}], x], x] Range[0, nmax]! // Rest
Table[(n - 1)! Sum[(-1)^k Binomial[n, k] n^(n - k - 1)/(n - k - 1)!, {k, 0, n - 1}], {n, 1, 21}]
Table[HypergeometricU[1 - n, 2, n], {n, 1, 21}]

Formula

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