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A196568 Binomial coefficients of the form C(k, 3) that are products of two other binomial coefficients of the form C(k, 3).

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%I A196568 #33 Jul 03 2024 09:00:11
%S A196568 560,19600,43680,893200,1521520,7207200,29269240,2845642800,
%T A196568 26595476600,249466897680
%N A196568 Binomial coefficients of the form C(k, 3) that are products of two other binomial coefficients of the form C(k, 3).
%C A196568 a(11), if it exists, > C(5*10^6, 3). - _D. S. McNeil_, Oct 26 2011
%H A196568 Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/1011.html">Problem of the month October 2011</a>
%e A196568      560 = C( 16, 3) = C( 8, 3) * C( 5, 3);
%e A196568    19600 = C( 50, 3) = C(16, 3) * C( 7, 3);
%e A196568    43680 = C( 65, 3) = C(14, 3) * C(10, 3);
%e A196568   893200 = C(176, 3) = C(30, 3) * C(12, 3).
%Y A196568 Subsequence of A364151 (more than 2 factors allowed).
%Y A196568 Cf. A188630 (analog for triangular numbers).
%K A196568 nonn,more
%O A196568 1,1
%A A196568 _Kausthub Gudipati_, Oct 04 2011
%E A196568 Name clarified by _Pontus von Brömssen_, Jun 22 2023