A055868 Fifth column of triangle A055864.

0, 0, 0, 0, 625, 9072, 153664, 2985984, 65610000, 1610510000, 43717791744, 1301153248512, 42150011228416, 1476840093750000, 55662776156160000, 2246042996417036288, 96619713808095645696, 4414553991933897025584, 213517926400000000000000, 10899570973272269168160000

Offset

1,5

Links

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

Formula

a(n) = A055864(n, 5).

a(n) = 0 for n = 1..4; a(n) = n^4*(n+1)^(n-5), n >= 5.

E.g.f.: (270*W(-x)^2 - 740*W(-x)^3 + 345*W(-x)^4 - 36*W(-x)^5 - 270*x^2 - 1280*x^3 - 3645*x^4 - 9216*x^5)/(4320*x), W(x) principal branch of Lambert's function.

a(n) ~ exp(1-11/(2*n)) * n^(n-1). - Amiram Eldar, Feb 07 2026

Mathematica

a[n_] := If[n < 5, 0, n^4*(n+1)^(n-5)]; Array[a, 20] (* Amiram Eldar, Feb 07 2026 *)

Crossrefs

Cf. A000272, A055864, A055865, A055070, A055867, A055858.

Sequence in context: A372845 A250832 A250827 * A016852 A016972 A156162

Adjacent sequences: A055865 A055866 A055867 * A055869 A055870 A055871

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 20 2000

Status

approved