A138898 Ratio of (2n-1)! to number of zeros in lower part of Sylvester matrix for polynomial of degree n with all nonzero coefficients.

60, 840, 30240, 1995840, 207567360, 31135104000, 6351561216000, 1689515283456000, 567677135241216000, 235018333989863424000, 117509166994931712000000, 69800445194989436928000000, 48581109855712648101888000000, 39156374543704394370121728000000, 36180490078382860397992476672000000, 37989514582302003417892100505600000000, 44979585265445572046784246998630400000000, 59642930061980828534035911520183910400000000

Offset

3,1

Links

Table of n, a(n) for n=3..20.

Formula

a(n) = (2n-1)!/((n-1)(n-2)). - R. J. Mathar, Apr 30 2008

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

Mathematica

Table[(2 n - 1)!/((n - 1)(n - 2)), {n, 3, 20}] - R. J. Mathar, Apr 30 2008

Crossrefs

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

Sequence in context: A063011 A008357 A259539 * A229368 A305625 A056321

Adjacent sequences: A138895 A138896 A138897 * A138899 A138900 A138901

Keyword

nonn

Author

Artur Jasinski, Apr 02 2008

Extensions

Edited and corrected by R. J. Mathar, Apr 30 2008

Status

approved