A036283 Write cosec x = 1/x + Sum e_n x^(2n-1)/(2n-1)!; sequence gives denominators of e_n.

6, 60, 126, 120, 66, 16380, 6, 4080, 7182, 3300, 138, 32760, 6, 1740, 42966, 8160, 6, 34545420, 6, 270600, 37926, 1380, 282, 1113840, 66, 3180, 21546, 3480, 354, 1703601900, 6, 16320, 194166, 60, 4686, 5043631320, 6, 60, 9954, 9200400, 498, 142981020, 6

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Comments

Denominator of [2^(2n-1) - 1] * Bernoulli(2n)/n.

Equals the denominators of the LS1[-2*m,n=1] matrix coefficients of A160487 for m = 1, 2, ... - Johannes W. Meijer, May 24 2009

The products of the first n terms of this sequence appear in the denominators of the a(n) formulas of the right hand columns of triangle A161739. See A000292 (n=1), A107963 (n=2), A161740 (n=3) and A161741 (n=4). The next six values of n show that this pattern persists. - Johannes W. Meijer, Oct 22 2009

Examples

			x^(-1)+1/6*x+7/360*x^3+31/15120*x^5+...
		

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 75 (4.3.68).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 75 (4.3.68).

Crossrefs

Cf. A036280-A036282.

Cf. A000292, A006953, A107963, A160487, A161739, A161740, A161741.

Programs

Maple

seq(denom((2^(2*n-1)-1)*bernoulli(2*n)/n),n=1..100); # Robert Israel, Oct 14 2016

PARI

a(n) = denominator((2^(2*n-1)-1)*bernfrac(2*n)/n) \\ Hugo Pfoertner, Dec 18 2022

Formula

Apparently a(n) = 6*A202318(n). - Hugo Pfoertner, Dec 18 2022

Extensions

Title corrected and offset changed by Johannes W. Meijer, May 21 2009

More terms, and edited by Robert Israel, Oct 14 2016