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A174159
Triangle read by rows. T(n, k) = 2 * Eulerian(n, k - 1) - binomial(n - 1, k - 1)* binomial(n, k - 1) / k.
2
1, 1, 1, 1, 5, 1, 1, 16, 16, 1, 1, 42, 112, 42, 1, 1, 99, 554, 554, 99, 1, 1, 219, 2277, 4657, 2277, 219, 1, 1, 466, 8390, 30748, 30748, 8390, 466, 1, 1, 968, 28880, 175292, 310616, 175292, 28880, 968, 1, 1, 1981, 95140, 907864, 2615416, 2615416, 907864, 95140
OFFSET
1,5
EXAMPLE
[ 1] 1;
[ 2] 1, 1;
[ 3] 1, 5, 1;
[ 4] 1, 16, 16, 1;
[ 5] 1, 42, 112, 42, 1;
[ 6] 1, 99, 554, 554, 99, 1;
[ 7] 1, 219, 2277, 4657, 2277, 219, 1;
[ 8] 1, 466, 8390, 30748, 30748, 8390, 466, 1;
[ 9] 1, 968, 28880, 175292, 310616, 175292, 28880, 968, 1;
[10] 1, 1981, 95140, 907864, 2615416, 2615416, 907864, 95140, 1981, 1;
MAPLE
# Works also if based on (0, 0).
T := (n, k) -> `if`(k = 0, k^n, 2*combinat:-eulerian1(n, k-1) - binomial(n-1, k-1)* binomial(n, k-1) / k):
for n from 1 to 6 do seq(T(n, k), k=1..n) od; # Peter Luschny, Jul 27 2022
MATHEMATICA
Needs["Combinatorica`"];
T[n_, m_] := 2*Eulerian[n, m - 1] - Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m;
Table[T[n, m], {n, 1, 10}, {m, 1, n}] // Flatten
CROSSREFS
Cf. A001263, A008292, A356118 (row sums).
Sequence in context: A292357 A156920 A174044 * A074060 A157637 A157181
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 10 2010
EXTENSIONS
Edited by Peter Luschny, Jul 27 2022
STATUS
approved