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A350262
Triangle read by rows. T(n, k) = B(n, n - k + 1) where B(n, k) = k^n * BellPolynomial(n, -1/k) for k > 0, if k = 0 then B(n, k) = k^n.
6
1, -1, -1, -2, -1, 0, -5, -1, 1, 1, 21, 25, 19, 9, 1, 1103, 674, 343, 128, 23, -2, 29835, 15211, 6551, 2133, 379, -25, -9, 739751, 331827, 123821, 33479, 3603, -1549, -583, -9, 16084810, 5987745, 1619108, 120865, -174114, -112975, -32600, -3087, 50
OFFSET
0,4
EXAMPLE
[0] 1
[1] -1, -1
[2] -2, -1, 0
[3] -5, -1, 1, 1
[4] 21, 25, 19, 9, 1
[5] 1103, 674, 343, 128, 23, -2
[6] 29835, 15211, 6551, 2133, 379, -25, -9
[7] 739751, 331827, 123821, 33479, 3603, -1549, -583, -9
[8] 16084810, 5987745, 1619108, 120865, -174114, -112975, -32600, -3087, 50
MAPLE
B := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, -1/k)):
A350262 := (n, k) -> B(n, n - k + 1):
seq(seq(A350262(n, k), k = 0..n), n = 0..8);
MATHEMATICA
B[n_, k_] := If[k == 0, k^n, k^n BellB[n, -1/k]]; T[n_, k_] := B[n, n - k + 1];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Dec 22 2021
STATUS
approved