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A227598 Number of lattice paths from {n}^7 to {0}^7 using steps that decrement one component such that for each point (p_1,p_2,...,p_7) we have p_1<=p_2<=...<=p_7.

%I A227598 #6 Nov 21 2016 12:50:13
%S A227598 1,1,1430,12310294,315051017342,16513520723284922,
%T A227598 1441565191975184121126,184570140930218389159747070,
%U A227598 31862864761563509123808857974124,6993293261428532974934599912795818724,1869718376047919275097272876105318640045150
%N A227598 Number of lattice paths from {n}^7 to {0}^7 using steps that decrement one component such that for each point (p_1,p_2,...,p_7) we have p_1<=p_2<=...<=p_7.
%H A227598 Vaclav Kotesovec, <a href="/A227598/b227598.txt">Table of n, a(n) for n = 0..48</a>
%F A227598 Conjecture: a(n) ~ 25 * sqrt(7) * 8^(7*n + 44) / (7^17 * 3^43 * Pi^3 * n^24). - _Vaclav Kotesovec_, Nov 21 2016
%p A227598 b:= proc(l) option remember; `if`(l[-1]=0, 1, add(add(b(subsop(
%p A227598       i=j, l)), j=`if`(i=1, 0, l[i-1])..l[i]-1), i=1..nops(l)))
%p A227598     end:
%p A227598 a:= n-> `if`(n=0, 1, b([n$7])):
%p A227598 seq(a(n), n=0..12);
%Y A227598 Column k=7 of A227578.
%K A227598 nonn
%O A227598 0,3
%A A227598 _Alois P. Heinz_, Jul 17 2013