A095674 Triangle read by rows, formed from product of Pascal's triangle (A007318) and Aitken's (or Bell's) triangle (A011971).

1, 2, 2, 5, 7, 5, 15, 22, 25, 15, 52, 74, 97, 97, 52, 203, 277, 372, 449, 411, 203, 877, 1154, 1524, 1948, 2209, 1892, 877, 4140, 5294, 6816, 8734, 10718, 11570, 9402, 4140, 21147, 26441, 33255, 41954, 52357, 62107, 64404, 50127, 21147, 115975, 142416

Offset: 0

Author

N. J. A. Sloane, based on a suggestion from Gary W. Adamson, Jun 22 2004

Keywords

• nonn
• tabl
• easy

Comments

These triangles are to be thought of as infinite lower-triangular matrices.

Examples

			Triangle begins:
1
2 2
5 7 5
15 22 25 15
52 74 97 97 52
203 277 372 449 411 203
		

Crossrefs

Cf. A007318, A011971, A095675. Row sums give A005494. First column is A000110.

Programs

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 *)

Extensions

More terms from Robert G. Wilson v, Jul 13 2004