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A263166 Number of lattice paths starting at {n}^8 and ending when any component equals 0, using steps that decrement one or more components by one.

%I A263166 #10 Apr 25 2020 14:48:13
%S A263166 1,255,277284181,7671206130046515,463841686707958609540881,
%T A263166 39946850792952097272345707272335,
%U A263166 4211153593189257990239568354710957472133,506051495006579137756029271328016744207715324419,66656513992169790340795231563272399566454175106315563265
%N A263166 Number of lattice paths starting at {n}^8 and ending when any component equals 0, using steps that decrement one or more components by one.
%H A263166 Alois P. Heinz, <a href="/A263166/b263166.txt">Table of n, a(n) for n = 0..20</a>
%p A263166 g():= seq(convert(n, base, 2)[1..8], n=257..511):
%p A263166 b:= proc(l) option remember;
%p A263166       `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
%p A263166     end:
%p A263166 a:= n-> b([n$8]):
%p A263166 seq(a(n), n=0..8);
%t A263166 g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 8]], {n, 2^8 + 1, 2^9 - 1}];
%t A263166 b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
%t A263166 a[n_] := b[Table[n, {8}]];
%t A263166 a /@ Range[0, 8] (* _Jean-François Alcover_, Apr 25 2020, after _Alois P. Heinz_ *)
%Y A263166 Column k=8 of A263159.
%K A263166 nonn
%O A263166 0,2
%A A263166 _Alois P. Heinz_, Oct 11 2015