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 A098564 #19 Aug 06 2024 02:18:31
%S A098564 10,15,21,28,35,36,45,55,56,66,78,84,91,105,126,136,153,165,171,190,
%T A098564 220,231,253,276,286,300,325,330,351,364,378,406,435,455,462,465,495,
%U A098564 496,528,560,561,595,630,666,680,703,715,741,780,792,816,820
%N A098564 Numbers that appear as binomial coefficients exactly 4 times.
%C A098564 Let f(k) be the sequence of numbers that appear as binomial coefficients exactly k times:
%C A098564 f(1) = {2}.
%C A098564 f(2) = A137905.
%C A098564 f(3) appears to be A000984 \ {1, 2}: central binomial coefficients greater than 2.
%C A098564 f(4) = this sequence.
%C A098564 f(5) appears to be empty.
%C A098564 f(6) = A098565.
%C A098564 f(7) appears to be empty.
%C A098564 f(8) begins with 3003.
%H A098564 T. D. Noe, <a href="/A098564/b098564.txt">Table of n, a(n) for n = 1..1000</a>
%t A098564 binmax = 10^5; dm = 100; Clear[f]; f[m_] := f[m] = (Join[Table[Binomial[n, k], {n, 1, m}, {k, 1, n-1}], Table[Table[{Binomial[n, 1], Binomial[n, 2]}, {2}], {n, m+1, binmax}]] // Flatten // Tally // Select[#, #[[1]] <= binmax && #[[2]] == 4&]&)[[All, 1]] // Sort; f[dm]; f[m = 2*dm]; While[f[m] != f[m-dm], Print[m]; m = m+dm]; f[m] (* _Jean-François Alcover_, Mar 10 2014 *)
%Y A098564 Cf. A000984, A098565, A137905.
%K A098564 nonn
%O A098564 1,1
%A A098564 _Paul D. Hanna_, Oct 27 2004