A227596 Number of lattice paths from {n}^5 to {0}^5 using steps that decrement one component such that for each point (p_1,p_2,...,p_5) we have p_1<=p_2<=...<=p_5.

1, 1, 132, 49100, 34426812, 36470203156, 51630369256916, 90650832149396184, 187978502469162658572, 445073778727031182727610, 1174228543974568589770758656, 3389786811049267225428045061056, 10559434352810002520295112134863908

Offset: 0

Author

Alois P. Heinz, Jul 17 2013

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..116

Crossrefs

Column k=5 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$5])):
seq(a(n), n=0..13);

Mathematica

b[l_] := b[l] = If[l[[-1]] == 0, 1, Sum[Sum[b[ReplacePart[l, i -> j]], {j, If[i == 1, 0, l[[i - 1]]], l[[i]] - 1}], {i, 1, Length[l]}]];
a[n_] := If[n == 0, 1, b[Array[n&, 5]]];
a /@ Range[0, 13] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *)

Formula

a(n) ~ 2*sqrt(5) * 6^(5*n+21) / (5^7 * 7^12 * Pi^2 * n^12). - Vaclav Kotesovec, Nov 20 2016