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A227604 Number of lattice paths from {7}^n to {0}^n using steps that decrement one component such that for each point (p_1,p_2,...,p_n) we have p_1<=p_2<=...<=p_n.

%I A227604 #6 Nov 23 2016 17:09:43
%S A227604 1,64,65445,312077474,3848596333400,90650832149396184,
%T A227604 3418868469576233694591,184570140930218389159747070,
%U A227604 13220723286785303728967102618052,1190606938488172095512348078940830464,129559009610760457771091688202936893773393
%N A227604 Number of lattice paths from {7}^n to {0}^n using steps that decrement one component such that for each point (p_1,p_2,...,p_n) we have p_1<=p_2<=...<=p_n.
%H A227604 Vaclav Kotesovec, <a href="/A227604/b227604.txt">Table of n, a(n) for n = 0..38</a>
%F A227604 Conjecture: a(n) ~ 2^4 * 5^2 * 7^(7*n + 85/2) / (6^37 * Pi^3 * n^24). - _Vaclav Kotesovec_, Nov 23 2016
%p A227604 b:= proc(l) option remember; `if`(l[-1]=0, 1, add(add(b(subsop(
%p A227604       i=j, l)), j=`if`(i=1, 0, l[i-1])..l[i]-1), i=1..nops(l)))
%p A227604     end:
%p A227604 a:= n-> `if`(n=0, 1, b([7$n])):
%p A227604 seq(a(n), n=0..11);
%Y A227604 Row n=7 of A227578.
%K A227604 nonn
%O A227604 0,2
%A A227604 _Alois P. Heinz_, Jul 17 2013