A227603 - OEIS

A227603

Number of lattice paths from {6}^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 #6 Nov 21 2016 16:08:32

%S 1,32,8925,8285506,16104165970,51630369256916,237791136700913751,

%T 1441565191975184121126,10844768238749437970393066,

%U 97106818062816381529413045436,1003769793669980634048599763674485,11703712713157396870910671640141678850

%N Number of lattice paths from {6}^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 Vaclav Kotesovec, <a href="/A227603/b227603.txt">Table of n, a(n) for n = 0..40</a>

%F Conjecture: a(n) ~ 2^(5/2) * 6^(6*n + 67/2) / (5^29 * Pi^(5/2) * n^(35/2)). - _Vaclav Kotesovec_, Nov 21 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([6$n])):

%p seq(a(n), n=0..12);

%Y Row n=6 of A227578.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jul 17 2013