OFFSET
0,3
LINKS
Alois P. Heinz, Rows n = 0..200, flattened
EXAMPLE
Triangle T(n,k) begins:
: 1;
: 1;
: 2, 1;
: 5, 2;
: 14, 9, 1;
: 43, 28, 3;
: 141, 114, 21, 1;
: 490, 421, 82, 4;
: 1785, 1750, 442, 38, 1;
: 6789, 7114, 1941, 180, 5;
: 26809, 30854, 9868, 1210, 60, 1;
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, (x+k*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:
seq(seq(T(n, k), k=0..n/2), n=0..13);
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, (x + k*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_] := T[n, k] = Sum[A[n, i]*(-1)^(k-i)*Binomial[k, i], {i, 0, k}]/ k!;
Table[T[n, k], {n, 0, 13}, {k, 0, n/2}] // Flatten (* Jean-François Alcover, Jun 06 2018, from Maple *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, May 25 2015
STATUS
approved