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Search: id:A091811
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| A091811 |
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Array read by rows: T(n,k) = binomial(n+k-2,k-1)*binomial(2*n-1,n-k). |
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| 1, 3, 2, 10, 15, 6, 35, 84, 70, 20, 126, 420, 540, 315, 70, 462, 1980, 3465, 3080, 1386, 252, 1716, 9009, 20020, 24024, 16380, 6006, 924, 6435, 40040, 108108, 163800, 150150, 83160, 25740, 3432, 24310, 175032, 556920, 1021020, 1178100, 875160
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Alternating sum of elements of n-th row = 1
If a certain event has a probability p of occurring in any given trial, the probability of its occurring at least n times in 2n-1 trials is sum_{k=1..n} T(n,k)*(-1)^(k-1)*p^(n+k-1). For example, the probability of its occurring at least 4 out of 7 times is 35p^4-84p^5+70p^6-20p^7. - Matthew Vandermast (ghodges14(AT)comcast.net), Jun 05 2004
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PROGRAM
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(PARI) T(x, y)=binomial(x+y-2, y-1)*binomial(2*x-1, x-y)
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CROSSREFS
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Cf. A001700 (first column), A002740 (second column), A000984 (main diagonal), A033876 (second diagonal).
Sequence in context: A113980 A095675 A006743 this_sequence A075856 A025520 A099946
Adjacent sequences: A091808 A091809 A091810 this_sequence A091812 A091813 A091814
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KEYWORD
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nonn,tabl,nice
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 18 2004
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