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A095674 Triangle read by rows, formed from product of Pascal's triangle (A007318) and Aitken's (or Bell's) triangle (A011971). 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 19 05:05 EDT 2019. Contains 323377 sequences. (Running on oeis4.)