Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
A227599
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.
2
1, 1, 4862, 213446666, 35566911169298, 14323116388173517180, 10844768238749437970393066, 13220723286785303728967102618052, 23408169635197679203800470649923362577, 55994660641252674524946692511672567020920313, 171650174624972457949599385901886660192203614365332
OFFSET
0,3
LINKS
FORMULA
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
MAPLE
b:= proc(l) option remember; `if`(l[-1]=0, 1, add(add(b(subsop(
i=j, l)), j=`if`(i=1, 0, l[i-1])..l[i]-1), i=1..nops(l)))
end:
a:= n-> `if`(n=0, 1, b([n$8])):
seq(a(n), n=0..10);
CROSSREFS
Column k=8 of A227578.
Sequence in context: A258397 A215549 A295442 * A321978 A147697 A208629
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 17 2013
STATUS
approved