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%I #13 Oct 21 2023 21:40:35
%S 34,89,104,359,398,2309,2729,3539,4619,8644,14135,36569,255959
%N Values of m for which C(m,k)+C(m,k+1)=C(m+1,k+1) divides C(m,2k+1) for some nonnegative integer k with 2k+1 <= m.
%C See A140601 which is the main entry for this sequence.
%C Some large terms of this sequence: 255959 (k=47), 618799 (k=25). - _Max Alekseyev_, Sep 19 2015
%e a(1)=34 because C(34,6) + C(34,7) = 1344904 + 5379616 = 6724520 divides C(34,13) = 927983760.
%o (Sage)
%o for m in range(100000):
%o for a in range(0, m//2):
%o if (binomial(m,2*a+1)%binomial(m+1,a+1) == 0):
%o print(m); break # _Robin Visser_, Oct 21 2023
%Y Cf. A140601, A140603.
%K hard,more,nonn
%O 1,1
%A _Andrew V. Sutherland_, May 18 2008
%E Offset corrected and a(12) added by _Max Alekseyev_, Aug 14 2017
%E a(13) from _Robin Visser_, Oct 21 2023
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