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A066320 Triangle read by rows: T(n, k) = binomial(n, k)*k^k*(n-k)^(n-k-1) k=0..n-1. 2
1, 2, 2, 9, 6, 12, 64, 36, 48, 108, 625, 320, 360, 540, 1280, 7776, 3750, 3840, 4860, 7680, 18750, 117649, 54432, 52500, 60480, 80640, 131250, 326592, 2097152, 941192, 870912, 945000, 1146880, 1575000, 2612736, 6588344, 43046721 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 68 (2.1.43).
LINKS
FORMULA
E.g.f.: -LambertW(-y)/(1+LambertW(-x*y)). - Vladeta Jovovic, Jan 26 2006
T(n, k) = n*binomial(n-1, k-1)*(k-1)^(k-1)*(n-k+1)^(n-k-1) assuming offset (1, 1). - Peter Luschny, Jan 12 2024
EXAMPLE
Triangle starts:
[1][ 1]
[2][ 2, 2]
[3][ 9, 6, 12]
[4][ 64, 36, 48, 108]
[5][ 625, 320, 360, 540, 1280]
[6][ 7776, 3750, 3840, 4860, 7680, 18750]
[7][ 117649, 54432, 52500, 60480, 80640, 131250, 326592]
[8][2097152, 941192, 870912, 945000, 1146880, 1575000, 2612736, 6588344]
PROG
(Julia) # Assuming offset (n=1, k=1).
T(n, k) = binomial(n-1, k-1)*(k-1)^(k-1)*n*(n-k+1)^(n-k-1)
for n in 1:9 (println([n], [T(n, k) for k in 1:n])) end
# Peter Luschny, Jan 12 2024
CROSSREFS
T = n * A185390 after proper alignment of offsets.
Columns 1, 2: A000169, A055541.
Main diagonal: A055897.
Row sums give A000312.
Sequence in context: A319129 A073315 A298597 * A005168 A256591 A011149
KEYWORD
nonn,tabl
AUTHOR
Christian G. Bower, Dec 13 2001
STATUS
approved

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Last modified March 29 09:32 EDT 2024. Contains 371268 sequences. (Running on oeis4.)