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Ratio of (2n-1)! to number of zeros in lower part of Sylvester matrix for polynomial of degree n with all nonzero coefficients.
3

%I #7 Jul 28 2024 00:16:15

%S 60,840,30240,1995840,207567360,31135104000,6351561216000,

%T 1689515283456000,567677135241216000,235018333989863424000,

%U 117509166994931712000000,69800445194989436928000000,48581109855712648101888000000,39156374543704394370121728000000,36180490078382860397992476672000000,37989514582302003417892100505600000000,44979585265445572046784246998630400000000,59642930061980828534035911520183910400000000

%N Ratio of (2n-1)! to number of zeros in lower part of Sylvester matrix for polynomial of degree n with all nonzero coefficients.

%F a(n) = (2n-1)!/((n-1)(n-2)). - _R. J. Mathar_, Apr 30 2008

%F Sum_{n=3..oo} 1/a(n) = (3*cosh(1) + 10*sinh(1) - 6*e)/4 = 0.0178907175323686230239526350278045532... . - _Stefano Spezia_, Jul 27 2024

%t Table[(2 n - 1)!/((n - 1)(n - 2)), {n, 3, 20}] - _R. J. Mathar_, Apr 30 2008

%Y Cf. A002378, A009445, A007878, A138896, A138898.

%K nonn

%O 3,1

%A _Artur Jasinski_, Apr 02 2008

%E Edited and corrected by _R. J. Mathar_, Apr 30 2008