A247504 Square array read by antidiagonals, A(n,k) = k!*[x^k]((1-Sum_{j=1..n} x^j)^(-1)), (n>=0,k>=0).

1, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 4, 6, 0, 1, 1, 4, 18, 24, 0, 1, 1, 4, 24, 120, 120, 0, 1, 1, 4, 24, 168, 960, 720, 0, 1, 1, 4, 24, 192, 1560, 9360, 5040, 0, 1, 1, 4, 24, 192, 1800, 17280, 105840, 40320, 0, 1, 1, 4, 24, 192, 1920, 20880, 221760, 1370880, 362880, 0

Offset: 0

Author

Peter Luschny, Nov 03 2014

Keywords

• nonn
• tabl

Examples

			n\k[0][1][2] [3]  [4]   [5]    [6]     [7]      [8]       [9]
[0] 1, 0, 0,  0,   0,    0,     0,      0,       0,        0
[1] 1, 1, 2,  6,  24,  120,   720,   5040,   40320,   362880 [A000142]
[2] 1, 1, 4, 18, 120,  960,  9360, 105840, 1370880, 19958400 [A005442]
[3] 1, 1, 4, 24, 168, 1560, 17280, 221760, 3265920, 54069120
[.] .  .  .  .  .   .   .   .    .    .    .     .     .
oo] 1, 1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280 [A002866]
'
As a triangular array, starts:
1,
1, 0,
1, 1, 0,
1, 1, 2, 0,
1, 1, 4, 6,  0,
1, 1, 4, 18, 24,  0,
1, 1, 4, 24, 120, 120, 0,
1, 1, 4, 24, 168, 960, 720, 0.
		

Crossrefs

Cf. A247505, A247506, A002866, A000142, A005442.

Programs

Maple

A := (n,k) -> k!*coeff(series((1-add(x^j, j=1..n))^(-1),x,k+2),x,k): seq(print(seq(A(n,k), k=0..9)), n=0..7);