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Sequence of the Day for August 11

A001020:
 11 n, n   ≥   0
.
{ 1, 11, 121, 1331, 14641, 161051, 1771561, ... }

In the classic Star Trek episode “The Trouble with Tribbles,” Spock estimates the growth of the Tribble population aboard the Enterprise thus: “1,771,561. That’s assuming one tribble, multiplying with an average litter of 10, producing a new generation every 12 hours over a period of three days.”

Note that for
 n = 0
to 4 you get numbers which are concatenated single digit (base 10) binomial coefficients, while for
 n   ≥   5
some binomial coefficients are now more than single digit (base 10) and thus overlap, e.g.
1
5
10
10
5
1
------
161051

Setting
 x = 10
and
 y = 1
in
(x + y)n =
 n ∑ k   = 0

(  nk  ) xk yn  − k

explains why this is so.