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A174183
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a(n) is the period k such that binomial(m, n) (mod 10) = binomial(m + k, n) (mod 10).
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2
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1, 10, 20, 60, 240, 1200, 7200, 50400, 403200, 3628800, 36288000, 399168000, 4790016000, 62270208000, 871782912000, 13076743680000, 209227898880000, 3556874280960000, 64023737057280000, 1216451004088320000
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OFFSET
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0,2
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COMMENTS
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a(n) is the period (mod 10) of the numbers in each column n of Pascal's triangle.
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
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LINKS
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FORMULA
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p(0)=1, and p(k) = 10*k ! for k >=1.
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EXAMPLE
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x(0)= 0.C(1,0)C(2,0)C(3,0) ... = 0.11111111111... and p(0)=1 ;
x(1)= 0.C(1,1)C(2,1)C(3,1) ... = 0.12345678901234... and p(1) = 10 ;
x(2)= 0.C(2,2)C(3,2)C(4,2) ... = 0.13605186556815063100 13605186556815063100... and p(2)=20.
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MAPLE
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for a from 0 to 40 do:u:=10*a!:print(u):od:
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MATHEMATICA
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CROSSREFS
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Cf. A002415, A007318, A002024, A000096, A000124, A002378, A000292, A000330, A055998, A055999, A056000, A056115, A056119, A056121, A056126, A051942, A101859, A001477.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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Additional comments, and errors in examples corrected by Michel Lagneau, May 07 2010
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STATUS
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approved
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