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A225221 Number of lattice paths without interior points from {4}^n to {0}^n using steps that decrement one component by 1.

%I A225221 #9 Sep 09 2016 14:08:32
%S A225221 1,0,2,2550,8059800,57010275000,801652441590000,20393765925943410000,
%T A225221 872251852597491366000000,59194435154364480600630000000,
%U A225221 6083868079208428011546743700000000,911478727065442542708032537906700000000,192819174440695429545254134608441231600000000
%N A225221 Number of lattice paths without interior points from {4}^n to {0}^n using steps that decrement one component by 1.
%C A225221 An interior point p = (p_1, ..., p_n) has n>0 components with 0<p_i<4 for 1<=i<=n.
%H A225221 Alois P. Heinz, <a href="/A225221/b225221.txt">Table of n, a(n) for n = 0..45</a>
%p A225221 b:= proc(n, l) option remember; local m; m:= nops(l);
%p A225221       `if`(m=0 or l[m]=0, 1, `if`(l[1]>0 and l[m]<n, 0,
%p A225221        add(`if`(l[i]=0, 0, b(n, sort(subsop(i=l[i]-1, l)))), i=1..m)))
%p A225221     end:
%p A225221 a:= n-> b(4, [4$n]):
%p A225221 seq(a(n), n=0..12);
%Y A225221 Row n=4 of A225094.
%K A225221 nonn
%O A225221 0,3
%A A225221 _Alois P. Heinz_, May 02 2013