A292898 Array read by ascending antidiagonals, A(m, n) = Sum_{k=1..m}(-1)^(k-n-m)* hypergeom([k, k-n-m], [], 1) for m>=1 and n>=0.

1, 1, 0, 3, 2, 1, 8, 7, 5, 2, 31, 30, 27, 20, 9, 147, 146, 142, 129, 97, 44, 853, 852, 847, 826, 755, 574, 265, 5824, 5823, 5817, 5786, 5652, 5187, 3973, 1854, 45741, 45740, 45733, 45690, 45463, 44462, 40923, 31520, 14833

Offset: 0

Author

Peter Luschny, Oct 05 2017

Keywords

• nonn
• tabl

Examples

			Array starts:
[m\n]   0       1      2       3        4         5          6
-------------------------------------------------------------------
[1]     1,      0,     1,      2,       9,       44,       265, ...  [A000166]
[2]     1,      2,     5,     20,      97,      574,      3973, ...  [A259834(n+2)]
[3]     3,      7,    27,    129,     755,     5187,     40923, ...  [A292897]
[4]     8,     30,   142,    826,    5652,    44462,    394970, ...
[5]    31,    146,   847,   5786,   45463,   403514,   3990679, ...
[6]   147,    852,  5817,  45690,  405423,  4008768,  43692933, ...
[7]   853,   5823, 45733, 405779, 4012101, 43727687, 520723477, ...
  A003470,A193464,A293295.
Displayed as a triangle:
[1]     1;
[2]     1,      0;
[3]     3,      2,     1;
[4]     8,      7,     5,    2;
[5]    31,     30,    27,   20,    9;
[6]   147,    146,   142,  129,   97,   44;
[7]   853,    852,   847,  826,  755,  574,  265;
[8]  5824,   5823,  5817, 5786, 5652, 5187, 3973, 1854;
  A003470,A193464,A293295.
This triangle has row sums A193463.
		

Crossrefs

Cf. A000166, A003470, A193463, A193464, A259834, A292897, A293295.

Programs

Maple

A := (m, n) -> add((-1)^(k-n-m)*hypergeom([k, k-n-m], [], 1), k=1..m):
seq(lprint(seq(simplify(A(m, n)), n=0..6)), m=1..7);

Mathematica

A[m_, n_] :=  Sum[(-1)^(k-n-m) HypergeometricPFQ[{k, k-n-m},{}, 1], {k, 1, m} ];
Table[Table[A[m, n], {n,0,6}], {m,1,7}]