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 A263159 Number A(n,k) of lattice paths starting at {n}^k and ending when k or any component equals 0, using steps that decrement one or more components by one; square array A(n,k), n>=0, k>=0, read by antidiagonals. 19
 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 13, 1, 1, 1, 15, 157, 63, 1, 1, 1, 31, 2101, 5419, 321, 1, 1, 1, 63, 32461, 717795, 220561, 1683, 1, 1, 1, 127, 580693, 142090291, 328504401, 9763807, 8989, 1, 1, 1, 255, 11917837, 39991899123, 944362553521, 172924236255, 454635973, 48639, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Alois P. Heinz, Antidiagonals n = 0..20, flattened EXAMPLE Square array A(n,k) begins:   1, 1,    1,       1,            1,                1, ...   1, 1,    3,       7,           15,               31, ...   1, 1,   13,     157,         2101,            32461, ...   1, 1,   63,    5419,       717795,        142090291, ...   1, 1,  321,  220561,    328504401,     944362553521, ...   1, 1, 1683, 9763807, 172924236255, 7622403922836151, ... MAPLE s:= proc(n) option remember; `if`(n=0, {[]},       map(x-> [[x[], 0], [x[], 1]][], s(n-1)))     end: b:= proc(l) option remember; `if`(l=[] or l[1]=0, 1,        add((p-> `if`(p[1]<0, 0, `if`(p[1]=0, 1, b(p)))        )(sort(l-x)), x=s(nops(l)) minus {[0\$nops(l)]}))     end: A:= (n, k)-> b([n\$k]): seq(seq(A(n, d-n), n=0..d), d=0..10); CROSSREFS Columns k=0+1, 2-10 give: A000012, A001850, A115866, A263162, A263163, A263164, A263165, A263166, A263167, A263168. Rows n=0-1 give: A000012, A255047. Main diagonal gives A263160. Cf. A210472, A225094, A227578, A227655, A229142, A229345, A262809. Sequence in context: A081297 A110180 A005765 * A229142 A156535 A243748 Adjacent sequences:  A263156 A263157 A263158 * A263160 A263161 A263162 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Oct 11 2015 STATUS approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)