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A095674
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Triangle read by rows, formed from product of Pascal's triangle (A007318) and Aitken's (or Bell's) triangle (A011971).
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1
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| These triangles are to be thought of as infinite lower-triangular matrices.
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EXAMPLE
| Triangle begins:
1
2 2
5 7 5
15 22 25 15
52 74 97 97 52
203 277 372 449 411 203
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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]] (from Robert G. Wilson v Jul 12 2004)
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CROSSREFS
| Cf. A007318, A011971, A095675. Row sums give A005494. First column is A000110.
Sequence in context: A021447 A136536 A023507 * A058123 A035586 A188623
Adjacent sequences: A095671 A095672 A095673 * A095675 A095676 A095677
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), based on a suggestion from Gary Adamson, Jun 22 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 13 2004
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