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 A289481 Number A(n,k) of Dyck paths of semilength k*n and height n; square array A(n,k), n>=0, k>=0, read by antidiagonals. 12
 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 7, 1, 0, 1, 1, 31, 57, 1, 0, 1, 1, 127, 1341, 484, 1, 0, 1, 1, 511, 26609, 59917, 4199, 1, 0, 1, 1, 2047, 497845, 5828185, 2665884, 36938, 1, 0, 1, 1, 8191, 9096393, 517884748, 1244027317, 117939506, 328185, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS For fixed k > 1, A(n,k) ~ 2^(2*k*n + 3) * k^(2*k*n + 1/2) / ((k-1)^((k-1)*n + 1/2) * (k+1)^((k+1)*n + 7/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 14 2017 LINKS Alois P. Heinz, Antidiagonals n = 0..80, flattened EXAMPLE Square array A(n,k) begins:   1, 1,    1,       1,          1,            1, ...   0, 1,    1,       1,          1,            1, ...   0, 1,    7,      31,        127,          511, ...   0, 1,   57,    1341,      26609,       497845, ...   0, 1,  484,   59917,    5828185,    517884748, ...   0, 1, 4199, 2665884, 1244027317, 517500496981, ... MAPLE b:= proc(x, y, k) option remember;       `if`(x=0, 1, `if`(y>0, b(x-1, y-1, k), 0)+       `if`(y <  min(x-1, k), b(x-1, y+1, k), 0))     end: A:= (n, k)-> `if`(n=0, 1, b(2*n*k, 0, n)-b(2*n*k, 0, n-1)): seq(seq(A(n, d-n), n=0..d), d=0..12); MATHEMATICA b[x_, y_, k_]:=b[x, y, k]=If[x==0, 1, If[y>0, b[x - 1, y - 1, k], 0] + If[y

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)