A227604 Number of lattice paths from {7}^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, 64, 65445, 312077474, 3848596333400, 90650832149396184, 3418868469576233694591, 184570140930218389159747070, 13220723286785303728967102618052, 1190606938488172095512348078940830464, 129559009610760457771091688202936893773393

Offset: 0

Author

Alois P. Heinz, Jul 17 2013

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..38

Crossrefs

Row n=7 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([7$n])):
seq(a(n), n=0..11);

Formula

Conjecture: a(n) ~ 2^4 * 5^2 * 7^(7*n + 85/2) / (6^37 * Pi^3 * n^24). - Vaclav Kotesovec, Nov 23 2016