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 A162444 Denominators of the BG1[ -5,n] coefficients of the BG1 matrix 1

%I #3 Jun 16 2016 23:27:39

%S 1,1,3,5,35,9,231,143,6435,12155,3553,88179,96577,1300075,5014575,

%T 102051,100180065,116680311,2268783825,210388475,6892326441,

%U 67282234305,17534158031,39583801575,8061900920775,169906729083

%N Denominators of the BG1[ -5,n] coefficients of the BG1 matrix

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

%C 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).

%F 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)!.

%e The first few formulas for the BG1[1-2*m,n] matrix coefficients are:

%e BG1[ -1,n] = (1)*4^(n-1)*(n-1)!^2/(2*n-2)!

%e BG1[ -3,n] = (1-2*n)*4^(n-1)*(n-1)!^2/(2*n-2)!

%e BG1[ -5,n] = (1-8*n+12*n^2)*4^(n-1)*(n-1)!^2/(2*n-2)!

%e BG1[ -7,n] = (1-2*n+60*n^2-120*n^3)*4^(n-1)*(n-1)!^2/(2*n-2)!

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

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

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

%K easy,frac,nonn

%O 1,3

%A _Johannes W. Meijer_, Jul 06 2009

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Last modified September 9 07:24 EDT 2024. Contains 375762 sequences. (Running on oeis4.)