OFFSET
0,2
COMMENTS
These triangles are to be thought of as infinite lower-triangular matrices.
EXAMPLE
Triangle begins:
1
2 2
5 7 5
15 22 25 15
52 74 97 97 52
203 277 372 449 411 203
MATHEMATICA
a[0, 0] = 1; a[n_, 0] := a[n - 1, n - 1]; a[n_, k_] := a[n, k] = If[k < n + 1, a[n, k - 1] + a[n - 1, k - 1], 0]; p[n_, r_] := If[r <= n + 1, Binomial[n, r], 0]; am = Table[ a[n, r], {n, 0, 9}, {r, 0, 9}]; pm = Table[p[n, r], {n, 0, 9}, {r, 0, 9}]; t = Flatten[pm.am]; Delete[ t, Position[t, 0]] (* Robert G. Wilson v, Jul 12 2004 *)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, based on a suggestion from Gary W. Adamson, Jun 22 2004
EXTENSIONS
More terms from Robert G. Wilson v, Jul 13 2004
STATUS
approved