A225111 Number of lattice paths without interior points from {n}^n to {0}^n using steps that decrement one component by 1.

1, 1, 2, 384, 8059800, 38606650125120, 71646205399259162031360, 78385944219935192681549282987212800, 71605824043564034004713155518007394441060661360000, 73473023853389304132357517396557811159635782691183541179936000000000

Offset

0,3

Comments

An interior point p = (p_1, ..., p_n) has n>0 components with 0<p_i<n for 1<=i<=n.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..12

Maple

b:= proc(n, l) option remember; local m; m:= nops(l);
      `if`(m=0 or l[m]=0, 1, `if`(l[1]>0 and l[m]<n, 0,
       add(`if`(l[i]=0, 0, b(n, sort(subsop(i=l[i]-1, l)))), i=1..m)))
    end:
a:= n-> b(n, [n$n]):
seq(a(n), n=0..9);

Mathematica

b[n_, l_] := b[n, l] = With[{m = Length[l]}, If[m == 0 || l[[m]] == 0, 1,
     If[l[[1]] > 0 && l[[m]] < n, 0, Sum[If[l[[i]] == 0, 0, b[n, Sort[
     ReplacePart[l, i -> l[[i]] - 1]]]], {i, 1, m}]]]];
a[n_] := b[n, Array[n&, n]];
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Apr 28 2022, after Alois P. Heinz *)

Crossrefs

Main diagonal of A225094.

Sequence in context: A171431 A280281 A225096 * A343698 A176937 A092701

Adjacent sequences: A225108 A225109 A225110 * A225112 A225113 A225114

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2013

Status

approved