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

0,2

Comments

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

Links

Table of n, a(n) for n=0..41.

Example

Triangle begins:
1
3 2
10 13 5
37 72 55 15
151 393 450 245 52

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 *)

Crossrefs

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

Sequence in context: A019242 A064367 A113980 * A340806 A226442 A300374

Adjacent sequences: A095672 A095673 A095674 * A095676 A095677 A095678

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