cp's OEIS Frontend

A227597 Number of lattice paths from {n}^6 to {0}^6 using steps that decrement one component such that for each point (p_1,p_2,...,p_6) we have p_1<=p_2<=...<=p_6.

%I A227597 #11 Nov 24 2016 08:15:06
%S A227597 1,1,429,750325,3086989927,22228291051255,237791136700913751,
%T A227597 3418868469576233694591,61845760669881132413037769,
%U A227597 1344481798162876850603732892817,33976468300798036566458244068649205,973569246761047672746215294808240044853
%N A227597 Number of lattice paths from {n}^6 to {0}^6 using steps that decrement one component such that for each point (p_1,p_2,...,p_6) we have p_1<=p_2<=...<=p_6.
%H A227597 Vaclav Kotesovec, <a href="/A227597/b227597.txt">Table of n, a(n) for n = 0..69</a>
%F A227597 Conjecture: a(n) ~ 5 * 7^(6*n+29) / (2^58 * 3^8 * Pi^(5/2) * n^(35/2)). - _Vaclav Kotesovec_, Nov 20 2016
%p A227597 b:= proc(l) option remember; `if`(l[-1]=0, 1, add(add(b(subsop(
%p A227597       i=j, l)), j=`if`(i=1, 0, l[i-1])..l[i]-1), i=1..nops(l)))
%p A227597     end:
%p A227597 a:= n-> `if`(n=0, 1, b([n$6])):
%p A227597 seq(a(n), n=0..13);
%Y A227597 Column k=6 of A227578.
%K A227597 nonn
%O A227597 0,3
%A A227597 _Alois P. Heinz_, Jul 17 2013