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.

1, 1, 429, 750325, 3086989927, 22228291051255, 237791136700913751, 3418868469576233694591, 61845760669881132413037769, 1344481798162876850603732892817, 33976468300798036566458244068649205, 973569246761047672746215294808240044853

Offset: 0

Author

Alois P. Heinz, Jul 17 2013

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..69

Crossrefs

Column k=6 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$6])):
seq(a(n), n=0..13);

Formula

Conjecture: a(n) ~ 5 * 7^(6*n+29) / (2^58 * 3^8 * Pi^(5/2) * n^(35/2)). - Vaclav Kotesovec, Nov 20 2016