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A362354
a(n) = 3*(n+3)^(n-1).
2
1, 3, 15, 108, 1029, 12288, 177147, 3000000, 58461513, 1289945088, 31813498119, 867763964928, 25949267578125, 844424930131968, 29713734098717811, 1124440102746243072, 45543381089624394897, 1966080000000000000000, 90125827485245075684223, 4372496892684322588065792
OFFSET
0,2
COMMENTS
This gives the third 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 = 3.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-function
FORMULA
a(n) = Sum_{k=0..n} |A137452(n, k)|*3^k = Sum_{k=0..n} binomial(n-1, k-1)*n^(n-k)*3^k, with the n = 0 term equal to 1 (not 0)).
E.g.f.: (LambertW(-x)/(-x))^3.
CROSSREFS
Column k=3 of A232006 (without leading zeros).
Cf. A137452.
Sequence in context: A105618 A120732 A245835 * A090351 A136221 A366180
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 24 2023
STATUS
approved