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 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. 3
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS 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 Cf. A000166, A003470, A193463, A193464, A259834, A292897, A293295. Sequence in context: A327917 A065602 A237596 * A198498 A016648 A104552 Adjacent sequences:  A292895 A292896 A292897 * A292899 A292900 A292901 KEYWORD nonn,tabl AUTHOR Peter Luschny, Oct 05 2017 STATUS approved

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Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)