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

0,2

Comments

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

Links

Table of n, a(n) for n=0..46.

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

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

Sequence in context: A021447 A136536 A023507 * A207981 A058123 A035586

Adjacent sequences: A095671 A095672 A095673 * A095675 A095676 A095677

Keyword

nonn,tabl,easy

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