A227598 Number of lattice paths from {n}^7 to {0}^7 using steps that decrement one component such that for each point (p_1,p_2,...,p_7) we have p_1<=p_2<=...<=p_7.

1, 1, 1430, 12310294, 315051017342, 16513520723284922, 1441565191975184121126, 184570140930218389159747070, 31862864761563509123808857974124, 6993293261428532974934599912795818724, 1869718376047919275097272876105318640045150

Offset: 0

Author

Alois P. Heinz, Jul 17 2013

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..48

Crossrefs

Column k=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([n$7])):
seq(a(n), n=0..12);

Formula

Conjecture: a(n) ~ 25 * sqrt(7) * 8^(7*n + 44) / (7^17 * 3^43 * Pi^3 * n^24). - Vaclav Kotesovec, Nov 21 2016