login
Smallest number occurring in exactly n rows of Pascal's triangle.
4

%I #20 Jul 22 2020 11:39:24

%S 2,6,120,3003

%N Smallest number occurring in exactly n rows of Pascal's triangle.

%C A059233(a(n)) = n and A059233(m) < n for m < a(n).

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Singmaster&#39;s_conjecture">Singmaster's conjecture</a>

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%e . n A180058 referred equal binomial coefficients (A007318) A059233

%e . - ------- ---------------------------------------------- -------

%e . 1 2 C (2, 1) 1

%e . 2 6 C (4, 2) C (6, 1) 2

%e . 3 120 C (10, 3) C (16, 2) C (120, 1) 3

%e . 4 3003 C (14, 6) C (15, 5) C (78, 2) C (3003, 1) 4 .

%o (Haskell)

%o import Data.List (elemIndex)

%o import Data.Maybe (fromJust)

%o a180058 = (+ 2) . fromJust . (`elemIndex` a059233_list)

%Y Cf. A185024, A182237, A098565, A003015, A003016.

%K nonn,more

%O 1,1

%A _Reinhard Zumkeller_, Dec 24 2012