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A174183 a(n) is the period k such that binomial(m, n) (mod 10) = binomial(m + k, n) (mod 10). 1
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 the 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

Table of n, a(n) for n=0..19.

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:

CROSSREFS

Cf. A002415, A007318, A002024, A000096, A000124, A002378, A000292, A000330, A055998, A055999, A056000, A056115, A056119, A056121, A056126, A051942, A101859, A001477.

Sequence in context: A067192 A030004 A271512 * A267554 A131726 A276764

Adjacent sequences:  A174180 A174181 A174182 * A174184 A174185 A174186

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Mar 11 2010

EXTENSIONS

Additional comments, and corrected errors in examples Michel Lagneau, May 07 2010

STATUS

approved

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Last modified March 29 18:39 EDT 2017. Contains 284273 sequences.