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A133289
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Riordan matrix T from A084358 (lists of sets of lists) inverse to the Riordan matrix TI = 2I-A129652 formed from A000262 (number of sets of lists) and reciprocal under a partition transform.
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2
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1, 1, 1, 5, 2, 1, 37, 15, 3, 1, 363, 148, 30, 4, 1, 4441, 1815, 370, 50, 5, 1, 65133, 26646, 5445, 740, 75, 6, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| T(n,k) is simply constructed from Pascal's triangle PT and A084358 through multiplication along the diagonals. Taking the matrix inverse gives TI = 2I-A129652 = PT times diagonal multiplication by -A000262 with the sign of the first term flipped to positive.
T and TI are also reciprocals under the list partition transform described in A133314.
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FORMULA
| T(n,k) = Binomial(n,k) * A084358(n-k)
E.g.f. = exp(xt) / { 2 - exp[x/(1-x)] }
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CROSSREFS
| Cf. A131202.
Sequence in context: A193590 A111544 A109281 * A107719 A174485 A021661
Adjacent sequences: A133286 A133287 A133288 * A133290 A133291 A133292
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Tom Copeland (tcjpn(AT)msn.com), Oct 16 2007, Nov 30 2007
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