A360174
Triangle read by rows. T(n, k) = (k + 1) * abs(Stirling1(n, k)).
Original entry on oeis.org
1, 0, 2, 0, 2, 3, 0, 4, 9, 4, 0, 12, 33, 24, 5, 0, 48, 150, 140, 50, 6, 0, 240, 822, 900, 425, 90, 7, 0, 1440, 5292, 6496, 3675, 1050, 147, 8, 0, 10080, 39204, 52528, 33845, 11760, 2254, 224, 9, 0, 80640, 328752, 472496, 336420, 134694, 31752, 4368, 324, 10
Offset: 0
Triangle T(n, k) starts:
[0] 1;
[1] 0, 2;
[2] 0, 2, 3;
[3] 0, 4, 9, 4;
[4] 0, 12, 33, 24, 5;
[5] 0, 48, 150, 140, 50, 6;
[6] 0, 240, 822, 900, 425, 90, 7;
[7] 0, 1440, 5292, 6496, 3675, 1050, 147, 8;
[8] 0, 10080, 39204, 52528, 33845, 11760, 2254, 224, 9;
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T := (n, k) -> (k + 1)*abs(Stirling1(n, k)):
for n from 0 to 8 do seq(T(n, k), k = 0..n) od;
A360205
Triangle read by rows. T(n, k) = (-1)^(n-k)*(k+1)*binomial(n, k)*pochhammer(1-n, n-k).
Original entry on oeis.org
1, 0, 2, 0, 4, 3, 0, 12, 18, 4, 0, 48, 108, 48, 5, 0, 240, 720, 480, 100, 6, 0, 1440, 5400, 4800, 1500, 180, 7, 0, 10080, 45360, 50400, 21000, 3780, 294, 8, 0, 80640, 423360, 564480, 294000, 70560, 8232, 448, 9, 0, 725760, 4354560, 6773760, 4233600, 1270080, 197568, 16128, 648, 10
Offset: 0
Triangle T(n, k) starts:
[0] 1;
[1] 0, 2;
[2] 0, 4, 3;
[3] 0, 12, 18, 4;
[4] 0, 48, 108, 48, 5;
[5] 0, 240, 720, 480, 100, 6;
[6] 0, 1440, 5400, 4800, 1500, 180, 7;
[7] 0, 10080, 45360, 50400, 21000, 3780, 294, 8;
[8] 0, 80640, 423360, 564480, 294000, 70560, 8232, 448, 9;
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T := (n, k) -> (-1)^(n - k)*(k + 1)*binomial(n, k)*pochhammer(1 - n, n - k):
seq(seq(T(n, k), k = 0..n), n = 0..9);
Showing 1-2 of 2 results.
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