A094094 Define x[1]...x[n] by the equations Sum_{j=1..n} x[j]^i = i, i=1..n; a(n) = n! * Sum_{j=1..n} x[j]^(n+1).

1, 5, 25, 139, 871, 6131, 48161, 419399, 4025071, 42359239, 486703009, 6081751259, 82345132871, 1203618149579, 18920122802881, 318578240878351, 5722495974697951, 109204791111380879, 2205128748183225281

Offset

1,2

Comments

Suggested by Example 2.24 in Lozansky and Rousseau. Hint: use Newton's equations.

References

E. Lozansky and C. Rousseau, Winning Solutions, Springer, 1996; see p. 103.

Links

Table of n, a(n) for n=1..19.

Formula

E.g.f.: (1-exp(x/(x-1)))/(1-x)^2. - Vladeta Jovovic, May 03 2004

a(n) = n!*(n+1-LaguerreL(n,1,1)) = Sum_{k=1..n} (-1)^(k+1)*n!/k!*binomial(n+1,k+1). - Vladeta Jovovic, Apr 27 2006

a(n) = (3*n - 1)*a(n-1) - n*(3*n - 4)*a(n-2) + (n-2)*(n-1)*n*a(n-3). - Vaclav Kotesovec, Nov 13 2017

Mathematica

Table[Sum[(-1)^(k+1)*n!/k!*Binomial[n+1, k+1], {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Nov 13 2017 *)

Crossrefs

Cf. A066668.

Sequence in context: A124891 A358504 A365772 * A344249 A081683 A064311

Adjacent sequences: A094091 A094092 A094093 * A094095 A094096 A094097

Keyword

nonn,easy

Author

N. J. A. Sloane, May 02 2004

Extensions

More terms from Vladeta Jovovic, May 03 2004

Status

approved