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%I #7 Nov 26 2016 08:32:00
%S 1,1,4862,213446666,35566911169298,14323116388173517180,
%T 10844768238749437970393066,13220723286785303728967102618052,
%U 23408169635197679203800470649923362577,55994660641252674524946692511672567020920313,171650174624972457949599385901886660192203614365332
%N Number of lattice paths from {n}^8 to {0}^8 using steps that decrement one component such that for each point (p_1,p_2,...,p_8) we have p_1<=p_2<=...<=p_8.
%H Vaclav Kotesovec, <a href="/A227599/b227599.txt">Table of n, a(n) for n = 0..37</a>
%F Conjecture: a(n) ~ 42 * sqrt(5) * 9^(8*n + 58) / (8^20 * 10^29 * n^(63/2) * Pi^(7/2)). - _Vaclav Kotesovec_, Nov 26 2016
%p b:= proc(l) option remember; `if`(l[-1]=0, 1, add(add(b(subsop(
%p i=j, l)), j=`if`(i=1, 0, l[i-1])..l[i]-1), i=1..nops(l)))
%p end:
%p a:= n-> `if`(n=0, 1, b([n$8])):
%p seq(a(n), n=0..10);
%Y Column k=8 of A227578.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jul 17 2013