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A263165 Number of lattice paths starting at {n}^7 and ending when any component equals 0, using steps that decrement one or more components by one.

%I A263165 #10 Apr 25 2020 14:48:07
%S A263165 1,127,11917837,15302345348179,38074918201135688881,
%T A263165 127994492508527577494290807,511210318493877135287739912958933,
%U A263165 2283244029676857615289372083169016508547,11029283913008516141643899112236047179180872449
%N A263165 Number of lattice paths starting at {n}^7 and ending when any component equals 0, using steps that decrement one or more components by one.
%H A263165 Alois P. Heinz, <a href="/A263165/b263165.txt">Table of n, a(n) for n = 0..20</a>
%p A263165 g():= seq(convert(n, base, 2)[1..7], n=129..255):
%p A263165 b:= proc(l) option remember;
%p A263165       `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
%p A263165     end:
%p A263165 a:= n-> b([n$7]):
%p A263165 seq(a(n), n=0..9);
%t A263165 g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 7]], {n, 2^7 + 1, 2^8 - 1}];
%t A263165 b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
%t A263165 a[n_] := b[Table[n, {7}]];
%t A263165 a /@ Range[0, 9] (* _Jean-François Alcover_, Apr 25 2020, after _Alois P. Heinz_ *)
%Y A263165 Column k=7 of A263159.
%K A263165 nonn
%O A263165 0,2
%A A263165 _Alois P. Heinz_, Oct 11 2015