A095675 Triangle read by rows, formed from product of Aitken's (or Bell's) triangle (A011971) and Pascal's triangle (A007318).

1, 3, 2, 10, 13, 5, 37, 72, 55, 15, 151, 393, 450, 245, 52, 674, 2202, 3365, 2748, 1166, 203, 3263, 12850, 24582, 26781, 17048, 5936, 877, 17007, 78488, 180477, 245971, 208856, 109107, 32243, 4140, 94828, 502327, 1349900, 2209695, 2346559, 1634998

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
3 2
10 13 5
37 72 55 15
151 393 450 245 52
		

Crossrefs

Cf. A007318, A011971, A095674. Row sums give A095676. First column is A005493.

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[am.pm]; Delete[ t, Position[t, 0]] (* Robert G. Wilson v, Jul 12 2004 *)

Extensions

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