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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
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
Sequence in context: A030004 A271512 A294473 * A267554 A337434 A328490
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.)