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 A174183 a(n) is the period k such that binomial(m, n) (mod 10) = binomial(m + k, n) (mod 10). 2
 1, 10, 20, 60, 240, 1200, 7200, 50400, 403200, 3628800, 36288000, 399168000, 4790016000, 62270208000, 871782912000, 13076743680000, 209227898880000, 3556874280960000, 64023737057280000, 1216451004088320000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the period (mod 10) of the numbers in each column n of Pascal's triangle. REFERENCES 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. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..449 Michel Lagneau, Proof Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014 FORMULA p(0)=1, and p(k) = 10*k ! for k >=1. EXAMPLE 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. MAPLE for a from 0 to 40 do:u:=10*a!:print(u):od: MATHEMATICA Join[{1}, Array[10#!&, 20]] (* Harvey P. Dale, Feb 18 2018 *) CROSSREFS Cf. A002415, A007318, A002024, A000096, A000124, A002378, A000292, A000330, A055998, A055999, A056000, A056115, A056119, A056121, A056126, A051942, A101859, A001477. Sequence in context: A030004 A271512 A294473 * A267554 A337434 A328490 Adjacent sequences: A174180 A174181 A174182 * A174184 A174185 A174186 KEYWORD nonn,base AUTHOR Michel Lagneau, Mar 11 2010 EXTENSIONS Additional comments, and errors in examples corrected by Michel Lagneau, May 07 2010 STATUS approved

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)