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A362356
a(n) = 5*(n + 5)^(n-1).
1
1, 5, 35, 320, 3645, 50000, 805255, 14929920, 313742585, 7378945280, 192216796875, 5497558138880, 171359481538165, 5784156907130880, 210264917311285295, 8192000000000000000, 340611592914758411505, 15056807481695325716480, 705250197803314844630515
OFFSET
0,2
COMMENTS
This gives the fifth exponential (also called binomial) convolution of {A000272(n+1)} = {A232006(n+1, 1)}, for n >= 0, with e.g.f. (LambertW(-x),(-x)) (LambertW is the principal branch of the Lambert W-function).
This is also the row polynomial P(n, x) of the unsigned triangle A137452, evaluated at x = 5.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-function
FORMULA
a(n) = Sum_{k=0..n} |A137452(n, k)|*5^k = Sum_{k=0..n} binomial(n-1, k-1)*n^(n-k)*5^k, with the n = 0 term equal to 1 (not 0)).
E.g.f.: (LambertW(-x)/(-x))^5.
CROSSREFS
Column k=5 of A232006.
Sequence in context: A124564 A260952 A349515 * A307679 A305306 A113342
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 24 2023
STATUS
approved