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

1,3

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).

Links

Table of n, a(n) for n=1..26.

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)!.

Example

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.

Sequence in context: A187993 A221158 A068111 * A305858 A261659 A346715

Adjacent sequences: A162441 A162442 A162443 * A162445 A162446 A162447

Keyword

easy,frac,nonn

Author

Johannes W. Meijer, Jul 06 2009

Status

approved