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.

1, 32, 8925, 8285506, 16104165970, 51630369256916, 237791136700913751, 1441565191975184121126, 10844768238749437970393066, 97106818062816381529413045436, 1003769793669980634048599763674485, 11703712713157396870910671640141678850

Offset: 0

Author

Alois P. Heinz, Jul 17 2013

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..40

Crossrefs

Row n=6 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([6$n])):
seq(a(n), n=0..12);

Formula

Conjecture: a(n) ~ 2^(5/2) * 6^(6*n + 67/2) / (5^29 * Pi^(5/2) * n^(35/2)). - Vaclav Kotesovec, Nov 21 2016