OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
FORMULA
a(n) = Sum_{k=0..floor(n/2)} A258310(n,k).
MAPLE
b:= proc(x, y, t, k) option remember; `if`(y>x or y<0, 0,
`if`(x=0, 1, b(x-1, y-1, false, k)*`if`(t, (k*x+y)/y, 1)
+b(x-1, y, false, k) +b(x-1, y+1, true, k)))
end:
A:= (n, k)-> b(n, 0, false, k):
T:= proc(n, k) option remember;
add(A(n, i)*(-1)^(k-i)*binomial(k, i), i=0..k)/k!
end:
a:= proc(n) option remember; add(T(n, k), k=0..n/2) end:
seq(a(n), n=0..30);
MATHEMATICA
b[x_, y_, t_, k_] := b[x, y, t, k] = If[y > x || y < 0, 0,
If[x == 0, 1, b[x - 1, y - 1, False, k]*If[t, (k*x + y)/y, 1]
+ b[x - 1, y, False, k] + b[x - 1, y + 1, True, k]]];
A[n_, k_] := b[n, 0, False, k];
T[n_, k_] := Sum[A[n, i] (-1)^(k - i) Binomial[k, i], {i, 0, k}]/k!;
a[n_] := Sum[T[n, k], {k, 0, n/2}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 01 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 25 2015
STATUS
approved