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A130478
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Triangle T(n,k) = n! / A130477(n,k).
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7
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1, 2, 2, 6, 3, 2, 24, 8, 3, 2, 120, 30, 8, 3, 2, 720, 144, 30, 8, 3, 2, 5040, 840, 144, 30, 8, 3, 2, 40320, 5760, 840, 144, 30, 8, 3, 2, 362880, 45360, 5760, 840, 144, 30, 8, 3, 2, 3628800, 403200, 45360, 5760, 840, 144, 30, 8, 3, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums = A130494: (1, 4, 11, 37, 163,...).
Sums of reciprocals of rows is 1 - Henry Bottomley (se16(AT)btinternet.com), Nov 05 2009.
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FORMULA
| Triangle(n,k) = n! / A130477(n,k); such that by rows as vector terms, (n-th row of A130477) dot (n-th row of A130478) = n-th row of A130493 = n! repeated n times. Triangle A130478 by rows = n! followed by the first (n-1)reversed terms of A001048: (2, 3, 8, 30, 144, 840,...). Left border = (1, 2, 6, 24, 120...); while all other columns = A001048: (2, 3, 8, 30,...). n-th row of the triangle = n terms of: (n!; (n-1!)+(n-2!); (n-2!)+(n-3!);...+ (1! + 1).
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EXAMPLE
| First few rows of the triangle are:
1;
2, 2;
6, 3, 2;
24, 8, 3, 2;
120, 30, 8, 3, 2;
720, 144, 30, 8, 3, 2;
5040, 840, 144, 30, 8, 3, 2;
...
Row 4 = (24, 8, 3, 2), terms such that (24, 8, 3, 2) dot (1, 3, 8, 12) = (24, 24, 24, 24), where (1, 3, 8, 12) = row 4 of A130477 and (24, 24, 24, 24) = row 4 of A130493.
Row 5 = (120, 30, 8, 3, 2) = 5! + (4!+3!) + (3!+2!) + (2!+1!) + (1!+1).
Row 5 = 120 followed by the first reversed 4 terms of A001048; i.e. 120 followed by 30, 8, 3, 2.
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CROSSREFS
| Cf. A130493, A001048, A130493, A130477.
Sequence in context: A196441 A130674 A100346 * A163890 A128623 A182701
Adjacent sequences: A130475 A130476 A130477 * A130479 A130480 A130481
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 31 2007
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EXTENSIONS
| Corrected and extended by Henry Bottomley (se16(AT)btinternet.com), Nov 05 2009
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