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A227602 Number of lattice paths from {5}^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.

%I A227602 #12 Dec 20 2020 07:47:02
%S A227602 1,16,1257,238636,77767945,36470203156,22228291051255,
%T A227602 16513520723284922,14323116388173517180,14071120934043157192832,
%U A227602 15313737501505148093502344,18156604289232210133044514152,23151467541948649805794187113781,31425801906523386705389663813716908
%N A227602 Number of lattice paths from {5}^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.
%H A227602 Vaclav Kotesovec, <a href="/A227602/b227602.txt">Table of n, a(n) for n = 0..60</a>
%F A227602 a(n) ~ 9 * 5^(5*n + 41/2) / (2^37 * Pi^2 * n^12). - _Vaclav Kotesovec_, Nov 21 2016
%p A227602 b:= proc(l) option remember; `if`(l[-1]=0, 1, add(add(b(subsop(
%p A227602       i=j, l)), j=`if`(i=1, 0, l[i-1])..l[i]-1), i=1..nops(l)))
%p A227602     end:
%p A227602 a:= n-> `if`(n=0, 1, b([5$n])):
%p A227602 seq(a(n), n=0..14);
%t A227602 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 A227602 a[n_] := If[n == 0, 1, b[Array[5&, n]]];
%t A227602 a /@ Range[0, 14] (* _Jean-François Alcover_, Dec 20 2020, after _Alois P. Heinz_ *)
%Y A227602 Row n=5 of A227578.
%K A227602 nonn
%O A227602 0,2
%A A227602 _Alois P. Heinz_, Jul 17 2013