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Search: id:A065352
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| A065352 |
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Smallest m such that C(2m,m) is divisible by (m+n)!/m!. |
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+0
1
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| 1, 3, 8, 19, 42, 153, 216, 375, 950, 3565, 4068, 12273, 12274, 31729, 122352
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For n=1 see Catalan-numbers:A000108.
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FORMULA
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C(2m, m)=A*((m+1)(m+2)...(m+n-1)(m+n)); a(n) is the smallest such m belonging to n: a(n)=Min(m; Mod(A000984(m), (m+n)!/m!)=0)
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EXAMPLE
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n=4: a(4)=19 means that C(38,19)=35345263800 is divisible by (19+1)(19+2)(19+3)(19+4)=23!/19!=20.21.22.23=215520; the quotient is 166315. Smaller (<19) central binomial coefficients are not divisible by such a product of 4 successive terms; the corresponding quotients for n=1,2,3,4,5,... are 1,1,13,166315,9120910752273999,...
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CROSSREFS
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Cf. A065344-A065350, A002503, A000108, A000984.
Sequence in context: A095681 A079583 A099050 this_sequence A161993 A008466 A102712
Adjacent sequences: A065349 A065350 A065351 this_sequence A065353 A065354 A065355
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 31 2001
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EXTENSIONS
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More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Apr 21 2002
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