A370706 Triangle read by rows: T(n, k) = binomial(n, k) * Pochhammer(n, k).

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

Links

Table of n, a(n) for n=0..44.

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

Adjacent sequences: A370703 A370704 A370705 * A370707 A370708 A370709

Keyword

nonn,tabl

Author

Peter Luschny, Feb 28 2024

Status

approved