OFFSET
1,1
COMMENTS
Let f(k) be the sequence of numbers that appear as binomial coefficients exactly k times:
f(1) = {2}.
f(2) = A137905.
f(3) appears to be A000984 \ {1, 2}: central binomial coefficients greater than 2.
f(4) = this sequence.
f(5) appears to be empty.
f(6) = A098565.
f(7) appears to be empty.
f(8) begins with 3003.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 27 2004
STATUS
approved