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A069466
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Triangle of numbers of square lattice walks that start and end at origin after 2k steps and contain exactly r steps to the east, possibly touching origin at intermediate stages.
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1
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2, 2, 6, 24, 6, 20, 180, 180, 20, 70, 1120, 2520, 1120, 70, 252, 6300, 25200, 25200, 6300, 252, 924, 33264, 207900, 369600, 207900, 33264, 924, 3432, 168168, 1513512, 4204200, 4204200, 1513512, 168168, 3432, 12870, 823680, 10090080, 40360320
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Recurrences: a(1, 0)=a(1, 1)=2 a(k, r)=2k*(2k-1)/(k-r)^2 *a(k-1, r) a(k, r)=(k+1-r)^2/r^2 *a(k, r-1) Explizit: a(k, r) = binomial(2k, k)*(binomial(k, r))^2 Sum[a(k, r), r=0, ..., k] = A002894(k)
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EXAMPLE
| a(4,1)=2520 because there are 2520 distinct lattice walks of length 2*4=8 starting and ending at the origin and containing exactly 1 step to the east. Let E, W, S, N denote the 4 possible directions, then NWSESSNN and SSNENNSW are examples of such walks.
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CROSSREFS
| Cf. A002894, A000984.
Sequence in context: A138801 A188958 * A141902 A143084 A188962 A076741
Adjacent sequences: A069463 A069464 A069465 * A069467 A069468 A069469
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KEYWORD
| easy,nice,nonn,tabl
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AUTHOR
| Martin Wohlgemuth (mail(AT)matroid.com), Mar 24 2002
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