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 A065352 Smallest m such that C(2m,m) is divisible by (m+n)!/m!. 0
 1, 3, 8, 19, 42, 153, 216, 375, 950, 3565, 4068, 12273, 12274, 31729, 122352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n=1 see Catalan-numbers:A000108. LINKS FORMULA 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) EXAMPLE 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,... CROSSREFS Cf. A065344-A065350, A002503, A000108, A000984. Sequence in context: A095681 A079583 A099050 * A161993 A008466 A102712 Adjacent sequences:  A065349 A065350 A065351 * A065353 A065354 A065355 KEYWORD nonn AUTHOR Labos E. (labos(AT)ana.sote.hu), Oct 31 2001 EXTENSIONS More terms from Naohiro Nomoto, Apr 21 2002 STATUS approved

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