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.

1, 1, 4862, 213446666, 35566911169298, 14323116388173517180, 10844768238749437970393066, 13220723286785303728967102618052, 23408169635197679203800470649923362577, 55994660641252674524946692511672567020920313, 171650174624972457949599385901886660192203614365332

Offset: 0

Author

Alois P. Heinz, Jul 17 2013

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..37

Crossrefs

Column k=8 of A227578.

Programs

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);

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