A366159 Triangle read by rows: T(n, k) = Sum_{i=0..k-2} (-1)^(i+2) * (k-i-1)^n * binomial(k,i).
1, 1, 5, 1, 13, 23, 1, 29, 121, 119, 1, 61, 479, 1081, 719, 1, 125, 1681, 6719, 10081, 5039, 1, 253, 5543, 35281, 90719, 100801, 40319, 1, 509, 17641, 168839, 665281, 1239839, 1088641, 362879, 1, 1021, 54959, 763561, 4339439, 12096001, 17539199, 12700801, 3628799
Offset: 2
Examples
Triangle begins: 1; 1, 5; 1, 13, 23; 1, 29, 121, 119; 1, 61, 479, 1081, 719; 1, 125, 1681, 6719, 10081, 5039; 1, 253, 5543, 35281, 90719, 100801, 40319; 1, 509, 17641, 168839, 665281, 1239839, 1088641, 362879; 1, 1021, 54959, 763561, 4339439, 12096001, 17539199, 12700801, 3628799; ...
Links
- Michael De Vlieger, Table of n, a(n) for n = 2..11176 (rows 2..150, flattened)
- Dmitry N. Kozlov, Stirling complexes, arXiv:2309.17142 [math.CO], 2023.
Programs
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Mathematica
Table[Sum[(-1)^(i + 2)*(k - i - 1)^n*Binomial[k, i], {i, 0, k - 2} ], {n, 2, 10}, {k, 2, n}] // Flatten (* Michael De Vlieger, Oct 02 2023 *) -
PARI
T(n, k) = sum(i=0, k-2, (-1)^(i+2) * (k-i-1)^n * binomial(k,i)); tabl(nn) = for (n=2, nn, for (k=2, n, print1(T(n,k), ", ")));