A162444 Denominators of the BG1[ -5,n] coefficients of the BG1 matrix.

1, 1, 3, 5, 35, 9, 231, 143, 6435, 12155, 3553, 88179, 96577, 1300075, 5014575, 102051, 100180065, 116680311, 2268783825, 210388475, 6892326441, 67282234305, 17534158031, 39583801575, 8061900920775, 169906729083

Offset: 1

Author

Johannes W. Meijer, Jul 06 2009

Keywords

• easy
• frac
• nonn

Comments

For the numerators of the BG1[ -5,n] coefficients see A162443.

We observe that BG1[ -3,n] = (-1)*A002595(n-1)/A055786(n-1), i.e. they equal the inverted coefficients of the series expansion of arcsin(x), and that BG1[ -1,n] = A046161(n-1)/A001790(n-1), i.e. they equal the inverted coefficients of the series expansion of 1/sqrt(1-x).

Examples

			The first few formulas for the BG1[1-2*m,n] matrix coefficients are:
BG1[ -1,n] = (1)*4^(n-1)*(n-1)!^2/(2*n-2)!
BG1[ -3,n] = (1-2*n)*4^(n-1)*(n-1)!^2/(2*n-2)!
BG1[ -5,n] = (1-8*n+12*n^2)*4^(n-1)*(n-1)!^2/(2*n-2)!
BG1[ -7,n] = (1-2*n+60*n^2-120*n^3)*4^(n-1)*(n-1)!^2/(2*n-2)!
		

Crossrefs

A162443 are the numerators of the BG1[ -5, n] matrix coefficients.

The BG1[ -3, n] equal A002595(n-1)/A055786(n-1) for n =>1.

The BG1[ -1, n] equal A046161(n-1)/A001790(n-1) for n =>1.

Formula

a(n) = denom(BG1[ -5,n]) and A162443(n) = numer(BG1[ -5,n]) with BG1[ -5,n] = 4^(n-1)*(1-8*n+12*n^2)*(n-1)!^2/ (2*n-2)!.