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A263167 Number of lattice paths starting at {n}^9 and ending when any component equals 0, using steps that decrement one or more components by one.

%I A263167 #10 Apr 25 2020 14:48:19
%S A263167 1,511,7229006221,4888774762356549331,8144781718207791515101819441,
%T A263167 20371729407721971932197861769050382551,
%U A263167 64254115995388375135778208276014009097192012661,235485313707274694851291521951126742198585792399471283971
%N A263167 Number of lattice paths starting at {n}^9 and ending when any component equals 0, using steps that decrement one or more components by one.
%H A263167 Alois P. Heinz, <a href="/A263167/b263167.txt">Table of n, a(n) for n = 0..15</a>
%p A263167 g():= seq(convert(n, base, 2)[1..9], n=513..1023):
%p A263167 b:= proc(l) option remember;
%p A263167       `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
%p A263167     end:
%p A263167 a:= n-> b([n$9]):
%p A263167 seq(a(n), n=0..7);
%t A263167 g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 9]], {n, 2^9+1, 2^10-1}];
%t A263167 b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
%t A263167 a[n_] := b[Table[n, {9}]];
%t A263167 a /@ Range[0, 7] (* _Jean-François Alcover_, Apr 25 2020, after _Alois P. Heinz_ *)
%Y A263167 Column k=9 of A263159.
%K A263167 nonn
%O A263167 0,2
%A A263167 _Alois P. Heinz_, Oct 11 2015