|
%I #14 Jan 06 2018 18:39:54
%S 1,1,0,3,2,1,8,7,5,2,31,30,27,20,9,147,146,142,129,97,44,853,852,847,
%T 826,755,574,265,5824,5823,5817,5786,5652,5187,3973,1854,45741,45740,
%U 45733,45690,45463,44462,40923,31520,14833
%N 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.
%e Array starts:
%e [m\n] 0 1 2 3 4 5 6
%e -------------------------------------------------------------------
%e [1] 1, 0, 1, 2, 9, 44, 265, ... [A000166]
%e [2] 1, 2, 5, 20, 97, 574, 3973, ... [A259834(n+2)]
%e [3] 3, 7, 27, 129, 755, 5187, 40923, ... [A292897]
%e [4] 8, 30, 142, 826, 5652, 44462, 394970, ...
%e [5] 31, 146, 847, 5786, 45463, 403514, 3990679, ...
%e [6] 147, 852, 5817, 45690, 405423, 4008768, 43692933, ...
%e [7] 853, 5823, 45733, 405779, 4012101, 43727687, 520723477, ...
%e A003470,A193464,A293295.
%e Displayed as a triangle:
%e [1] 1;
%e [2] 1, 0;
%e [3] 3, 2, 1;
%e [4] 8, 7, 5, 2;
%e [5] 31, 30, 27, 20, 9;
%e [6] 147, 146, 142, 129, 97, 44;
%e [7] 853, 852, 847, 826, 755, 574, 265;
%e [8] 5824, 5823, 5817, 5786, 5652, 5187, 3973, 1854;
%e A003470,A193464,A293295.
%e This triangle has row sums A193463.
%p A := (m, n) -> add((-1)^(k-n-m)*hypergeom([k, k-n-m], [], 1), k=1..m):
%p seq(lprint(seq(simplify(A(m, n)), n=0..6)), m=1..7);
%t A[m_, n_] := Sum[(-1)^(k-n-m) HypergeometricPFQ[{k, k-n-m},{}, 1], {k, 1, m} ];
%t Table[Table[A[m, n], {n,0,6}], {m,1,7}]
%Y Cf. A000166, A003470, A193463, A193464, A259834, A292897, A293295.
%K nonn,tabl
%O 0,4
%A _Peter Luschny_, Oct 05 2017
|
