A227596 - OEIS

%I #15 Dec 20 2020 07:48:43

%S 1,1,132,49100,34426812,36470203156,51630369256916,90650832149396184,

%T 187978502469162658572,445073778727031182727610,

%U 1174228543974568589770758656,3389786811049267225428045061056,10559434352810002520295112134863908

%N 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.

%H Vaclav Kotesovec, <a href="/A227596/b227596.txt">Table of n, a(n) for n = 0..116</a>

%F a(n) ~ 2*sqrt(5) * 6^(5*n+21) / (5^7 * 7^12 * Pi^2 * n^12). - _Vaclav Kotesovec_, Nov 20 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([n$5])):

%p seq(a(n), n=0..13);

%t 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]}]];

%t a[n_] := If[n == 0, 1, b[Array[n&, 5]]];

%t a /@ Range[0, 13] (* _Jean-François Alcover_, Dec 20 2020, after _Alois P. Heinz_ *)

%Y Column k=5 of A227578.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jul 17 2013