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A158793
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Triangle read by rows: product of A130595 and A092392 considered as infinite lower triangular arrays.
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3
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1, 1, 1, 3, 1, 1, 7, 4, 1, 1, 19, 9, 5, 1, 1, 51, 26, 11, 6, 1, 1, 141, 70, 34, 13, 7, 1, 1, 393, 197, 92, 43, 15, 8, 1, 1, 1107, 553, 265, 117, 53, 17, 9, 1, 1, 3139, 1570, 751, 346, 145, 64, 19, 10, 1, 1, 8953, 4476, 2156, 991, 441, 176, 76, 21, 11, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Riordan array (f(x), x*g(x)) where f(x) is the g.f. of A002426 and where g(x) is the g.f. of A005043. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 05 2009]
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FORMULA
| T(n,m) = sum_{k=m..n-1} A130595(n,k) * A092392(k+1,m+1), with the triangular interpretation of A092392.
Row sums: sum_{m=0..n-1} T(n,m) = A005773(n).
T(n,0) = A002426(n).
Conjecture: T(n,1) = A113682(n-1). [R. J. Mathar, Oct 06 2009]
Sum-{k, 0<=k<=n} T(n,k)*x^k = A002426(n), A005773(n+1), A000244(n), A126932(n) for x = 0,1,2,3 respectively. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 03 2009]
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EXAMPLE
| The first rows of the triangle are:
1;
1, 1;
3, 1, 1;
7, 4, 1, 1;
19, 9, 5, 1, 1;
51, 26, 11, 6, 1, 1;
141, 70, 34, 13, 7, 1, 1;
393, 197, 92, 43, 15, 8, 1, 1;
1107, 553, 265, 117, 53, 17, 9, 1, 1;
3139, 1570, 751, 346, 145, 64, 19, 10, 1, 1;
8953, 4476, 2156, 991, 441, 176, 76, 21, 11, 1, 1;
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CROSSREFS
| Cf. A046899, A007318.
Sequence in context: A121300 A128119 A158198 * A112996 A136621 A108625
Adjacent sequences: A158790 A158791 A158792 * A158794 A158795 A158796
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Mar 26 2009
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EXTENSIONS
| Simplified definition - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 06 2009
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