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A085484
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Symmetric square table, read by antidiagonals, such that the main diagonal is equal to the first row shift left: T(0,0)=1, T(0,k) = sum(m=0,k-1, C(k-1,m)*T(m,k-1-m)) when k>0; and T(n,k) = T(n-1,k) + T(n,k-1) when n>0, k>0.
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2
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1, 1, 1, 2, 2, 2, 8, 4, 4, 8, 40, 12, 8, 12, 40, 224, 52, 30, 30, 52, 224, 1368, 276, 72, 40, 72, 276, 1368, 9008, 1644, 348, 112, 112, 348, 1644, 9008, 63488, 10652, 1992, 460, 224, 460, 1992, 10652, 63488, 476160, 74140, 12644, 2452, 684, 684, 2452, 12644
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Antidiagonal sums give A085486. First row is A085485; table is symmetric under transpose, so that first column equals the first row. Second row gives partial sums of first row.
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EXAMPLE
| Rows begin:
....1 ....1 ....2 .....8 ....40 ...224 ..1368 ..9008 ...
....1 ....2 ....4 ....12 ....52 ...276 ..1644 .10652 ...
....2 ....4 ....8 ....20 ....72 ...348 ..1992 .12644 ...
....8 ...12 ...20 ....40 ...112 ...460 ..2452 .15096 ...
...40 ...52 ...72 ...112 ...224 ...684 ..3136 .18232 ...
..224 ..276 ..348 ...460 ...684 ..1368 ..4504 .22736 ...
.1368 .1644 .1992 ..2452 ..3136 ..4504 ..9008 .31744 ...
.9008 10652 12644 .15096 .18232 .22736 .31744 .63488 ...
63488 74140 86784 101880 120112 142848 174592 238080 ...
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CROSSREFS
| Cf. A085485 (first row and diagonal), A085486 (antidiagonal sums).
Sequence in context: A029605 A054271 A011202 * A116585 A008293 A185811
Adjacent sequences: A085481 A085482 A085483 * A085485 A085486 A085487
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 02 2003
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