A325146 A(n, k) = Stirling2(n + k, k)*A053657(n)*k!/(n + k)!, array read by ascending antidiagonals for n >= 0 and k >= 0.

1, 0, 1, 0, 1, 1, 0, 4, 2, 1, 0, 2, 14, 3, 1, 0, 48, 12, 30, 4, 1, 0, 16, 496, 36, 52, 5, 1, 0, 576, 288, 2064, 80, 80, 6, 1, 0, 144, 18288, 1656, 5832, 150, 114, 7, 1, 0, 3840, 8160, 145200, 5920, 13240, 252, 154, 8, 1

Offset: 0

Author

Peter Luschny, May 22 2019

Keywords

• nonn
• tabl

Examples

			[0] 1,   1,     1,      1,      1,       1,       1,        1, ... A000012
[1] 0,   1,     2,      3,      4,       5,       6,        7, ... A001477
[2] 0,   4,    14,     30,     52,      80,     114,      154, ... A049451
[3] 0,   2,    12,     36,     80,     150,     252,      392, ... A011379
[4] 0,  48,   496,   2064,   5832,   13240,   26088,    46536, ...
[5] 0,  16,   288,   1656,   5920,   16200,   37296,    76048, ...
[6] 0, 576, 18288, 145200, 654816, 2153280, 5775936, 13429248, ...
     A163176
		

Crossrefs

Rows include A001477, A049451, A011379. Columns include A163176.

Cf. A053657.

Programs

Maple

A := (n, k) -> Stirling2(n + k, k)*A053657(n)*k!/(n + k)!:
seq(seq(A(n - k, k), k=0..n), n=0..10);

Mathematica

a053657[n_] := Product[p^Sum[Floor[(n-1) / ((p-1) p^k)], {k, 0, n}], {p, Prime[Range[n]]}];
A[n_, k_] := StirlingS2[n+k, k] a053657[n+1] k! / (n+k)!;
Table[A[n-k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 21 2019 *)