OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
EXAMPLE
a(1) = 1: 1.
a(2) = 1: 21.
a(3) = 5: 132, 213, 231, 312, 321.
a(4) = 18: 1243, 1342, 1432, 2134, 2143, 2341, 2431, 3124, 3142, 3214, 3241, 3421, 4123, 4132, 4213, 4231, 4312, 4321.
MAPLE
g:= proc(u, o) option remember; `if`(u+o<2, u,
add(b(u-i, o+i-1), i=1..u) +add(g(u+i-1, o-i), i=1..o))
end:
b:= proc(u, o) option remember; `if`(u+o<2, 1-o,
u*(u+o-1)! +add(g(u+i-1, o-i), i=1..o))
end:
a:= n-> add(b(j-1, n-j), j=1..n):
seq(a(n), n=0..25);
MATHEMATICA
g[u_, o_] := g[u, o] = If[u + o < 2, u,
Sum[b[u - i, o + i - 1], {i, u}] +
Sum[g[u + i - 1, o - i], {i, o}]];
b[u_, o_] := b[u, o] = If[u + o < 2, 1 - o, u*(u + o - 1)! +
Sum[g[u + i - 1, o - i], {i, o}]];
a[n_] := Sum[b[j - 1, n - j], {j, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Aug 30 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 27 2013
STATUS
approved