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A370706
Triangle read by rows: T(n, k) = binomial(n, k) * Pochhammer(n, k).
2
1, 1, 1, 1, 4, 6, 1, 9, 36, 60, 1, 16, 120, 480, 840, 1, 25, 300, 2100, 8400, 15120, 1, 36, 630, 6720, 45360, 181440, 332640, 1, 49, 1176, 17640, 176400, 1164240, 4656960, 8648640, 1, 64, 2016, 40320, 554400, 5322240, 34594560, 138378240, 259459200
OFFSET
0,5
FORMULA
T(n, k) = A370707(n, k) / k!.
T(n, n) = Pochhammer(n, n) for n >= 0 (which is different from A000407(n)).
EXAMPLE
Triangle starts:
[0] 1;
[1] 1, 1;
[2] 1, 4, 6;
[3] 1, 9, 36, 60;
[4] 1, 16, 120, 480, 840;
[5] 1, 25, 300, 2100, 8400, 15120;
[6] 1, 36, 630, 6720, 45360, 181440, 332640;
[7] 1, 49, 1176, 17640, 176400, 1164240, 4656960, 8648640;
MAPLE
T := (n, k) -> binomial(n, k)*pochhammer(n, k):
seq(seq(T(n, k), k = 0..n), n = 0..8);
MATHEMATICA
T[n_, k_] := Binomial[n, k] Pochhammer[n, k];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten
CROSSREFS
Cf. A370707, A000407 (main diagonal), A278070 (row sums).
Sequence in context: A021688 A119439 A290823 * A090642 A100612 A322778
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Feb 28 2024
STATUS
approved