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A263163 Number of lattice paths starting at {n}^5 and ending when any component equals 0, using steps that decrement one or more components by one.

%I A263163 #9 Apr 25 2020 14:47:54
%S A263163 1,31,32461,142090291,944362553521,7622403922836151,
%T A263163 68836844233002312181,668865316589763487491811,
%U A263163 6842570537592835194176298241,72725938463068824904583496062671,796079042828286992045143086504942301,8920612967950147759634381671622287341331
%N A263163 Number of lattice paths starting at {n}^5 and ending when any component equals 0, using steps that decrement one or more components by one.
%H A263163 Alois P. Heinz, <a href="/A263163/b263163.txt">Table of n, a(n) for n = 0..75</a>
%p A263163 g():= seq(convert(n, base, 2)[1..5], n=33..63):
%p A263163 b:= proc(l) option remember;
%p A263163       `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
%p A263163     end:
%p A263163 a:= n-> b([n$5]):
%p A263163 seq(a(n), n=0..12);
%t A263163 g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 5]], {n, 2^5 + 1, 2^6 - 1}];
%t A263163 b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
%t A263163 a[n_] := b[Table[n, {5}]];
%t A263163 a /@ Range[0, 12] (* _Jean-François Alcover_, Apr 25 2020, after _Alois P. Heinz_ *)
%Y A263163 Column k=5 of A263159.
%K A263163 nonn
%O A263163 0,2
%A A263163 _Alois P. Heinz_, Oct 11 2015