A055070 Third column of triangle A055864.

0, 0, 9, 80, 900, 12348, 200704, 3779136, 81000000, 1948717100, 52027785216, 1527047909712, 48884036690944, 1695352148437500, 63331869759897600, 2535571976423919872, 108321063231221415936, 4918685157679434648876, 236584960000000000000000, 12016776998032676757896400

Offset

1,3

Links

Table of n, a(n) for n=1..20.

Formula

a(n) = A055864(n, 3).

a(1) = a(2) = 0; a(n) = n^2*(n+1)^(n-3), n >= 3.

E.g.f.: (3*W(-x)^2 - 2*W(-x)^3 - 3*x^2 - 8*x^3)/(12*x), W(x) principal branch of Lambert's function.

a(n) ~ exp(1-7/(2*n)) * n^(n-1). - Amiram Eldar, Feb 07 2026

Mathematica

a[n_] := n^2*(n+1)^(n-3); a[1] = a[2] = 0; Array[a, 20] (* Amiram Eldar, Feb 07 2026 *)

Crossrefs

Cf. A055864, A000272, A055865.

Sequence in context: A359921 A192214 A127265 * A143848 A393490 A317052

Adjacent sequences: A055067 A055068 A055069 * A055071 A055072 A055073

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 20 2000

Status

approved