This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A059233 #23 Feb 16 2025 08:32:43
%S A059233 1,1,1,1,2,1,1,1,2,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,
%T A059233 2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,2,1,1,1,
%U A059233 2,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1
%N A059233 Number of rows in which n appears in Pascal's triangle A007318.
%C A059233 Central binomial coefficients c = A000984(n) > 1 appear once in the middle column C(2n, n), and thereafter in one or more later rows to the left as C(r,k) and to the right as C(r, r-k), k < r/2; the last time in row r = c = C(c,1) = C(c,c-1). For these, a(n) = (A003016(n)+1)/2. For all other numbers n > 1, a(n) = A003016(n)/2. - _M. F. Hasler_, Mar 01 2023
%D A059233 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 93, #47.
%D A059233 C. S. Ogilvy, Tomorrow's Math. 2nd ed., Oxford Univ. Press, 1972, p. 96.
%H A059233 T. D. Noe, <a href="/A059233/b059233.txt">Table of n, a(n) for n=2..10000</a>
%H A059233 D. Singmaster, <a href="http://www.jstor.org/stable/2316907">How often does an integer occur as a binomial coefficient?</a>, Amer. Math. Monthly, 78 (1971), 385-386.
%H A059233 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PascalsTriangle.html">Pascal's Triangle</a>
%H A059233 Wikipedia, <a href="http://en.wikipedia.org/wiki/Singmaster's_conjecture">Singmaster's conjecture</a>
%H A059233 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A059233 a(A180058(n)) = n and a(m) < n for m < A180058(n); a(A182237(n)) = 2; a(A098565(n)) = 3. - _Reinhard Zumkeller_, Dec 24 2012
%F A059233 a(n) = ceiling(A003016(n)/2). - _M. F. Hasler_, Mar 01 2023
%e A059233 6 appears in both row 4 and row 6 in Pascal's triangle, therefore a(6) = 2.
%t A059233 nmax = 101; A007318 = Table[Binomial[n, k], {n, 0, nmax}, {k, 0, n}]; a[n_] := Position[A007318, n][[All, 1]] // Union // Length; Table[a[n], {n, 2, nmax}] (* _Jean-François Alcover_, Sep 09 2013 *)
%o A059233 (Haskell)
%o A059233 a059233 n = length $ filter (n `elem`) $
%o A059233 take (fromInteger n) $ tail a007318_tabl
%o A059233 a059233_list = map a059233 [2..]
%o A059233 -- _Reinhard Zumkeller_, Dec 24 2012
%o A059233 (PARI) A059233(n)=A003016(n)\/2 \\ _M. F. Hasler_, Mar 01 2023
%Y A059233 Cf. A003016, A003015.
%K A059233 easy,nice,nonn
%O A059233 2,5
%A A059233 _Fabian Rothelius_, Jan 20 2001