OFFSET
0,4
EXAMPLE
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, ...
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;
This triangle has row sums A193463.
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}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Oct 05 2017
STATUS
approved