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URL: https://oeis.org/A055868

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A055868
Fifth column of triangle A055864.
1
0, 0, 0, 0, 625, 9072, 153664, 2985984, 65610000, 1610510000, 43717791744, 1301153248512, 42150011228416, 1476840093750000, 55662776156160000, 2246042996417036288, 96619713808095645696, 4414553991933897025584, 213517926400000000000000, 10899570973272269168160000
OFFSET
1,5
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 20 2000
STATUS
approved