OFFSET
0,2
COMMENTS
This gives the fourth 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 = 4.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-function
Wikipedia, Lambert W function
FORMULA
a(n) = Sum_{k=0..n} |A137452(n, k)|*4^k = Sum_{k=0..n} binomial(n-1, k-1)*n^(n-k)*4^k, with the n = 0 term equal to 1 (not 0)).
E.g.f.: (LambertW(-x)/(-x))^4.
MATHEMATICA
Table[4(n+4)^(n-1), {n, 0, 20}] (* Harvey P. Dale, Jun 05 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 24 2023
STATUS
approved