

A098564


Numbers that appear as binomial coefficients exactly 4 times.


3



10, 15, 21, 28, 35, 36, 45, 55, 56, 66, 78, 84, 91, 105, 126, 136, 153, 165, 171, 190, 220, 231, 253, 276, 286, 300, 325, 330, 351, 364, 378, 406, 435, 455, 462, 465, 495, 496, 528, 560, 561, 595, 630, 666, 680, 703, 715, 741, 780, 792, 816, 820
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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) = A000984 (central binomial coefficients) except for first 2 terms: {1,2}.
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, n1}], 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[mdm], Print[m]; m = m+dm]; f[m] (* JeanFrançois Alcover, Mar 10 2014 *)


CROSSREFS

Cf. A000984, A098565, A137905.
Sequence in context: A115708 A068992 A325901 * A168103 A322045 A062691
Adjacent sequences: A098561 A098562 A098563 * A098565 A098566 A098567


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Oct 27 2004


STATUS

approved



