Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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