This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A162444 #5 Jul 22 2025 06:55:00 %S A162444 1,1,3,5,35,9,231,143,6435,12155,3553,88179,96577,1300075,5014575, %T A162444 102051,100180065,116680311,2268783825,210388475,6892326441, %U A162444 67282234305,17534158031,39583801575,8061900920775,169906729083 %N A162444 Denominators of the BG1[ -5,n] coefficients of the BG1 matrix. %C A162444 For the numerators of the BG1[ -5,n] coefficients see A162443. %C A162444 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 A162444 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 A162444 The first few formulas for the BG1[1-2*m,n] matrix coefficients are: %e A162444 BG1[ -1,n] = (1)*4^(n-1)*(n-1)!^2/(2*n-2)! %e A162444 BG1[ -3,n] = (1-2*n)*4^(n-1)*(n-1)!^2/(2*n-2)! %e A162444 BG1[ -5,n] = (1-8*n+12*n^2)*4^(n-1)*(n-1)!^2/(2*n-2)! %e A162444 BG1[ -7,n] = (1-2*n+60*n^2-120*n^3)*4^(n-1)*(n-1)!^2/(2*n-2)! %Y A162444 A162443 are the numerators of the BG1[ -5, n] matrix coefficients. %Y A162444 The BG1[ -3, n] equal A002595(n-1)/A055786(n-1) for n =>1. %Y A162444 The BG1[ -1, n] equal A046161(n-1)/A001790(n-1) for n =>1. %K A162444 easy,frac,nonn %O A162444 1,3 %A A162444 _Johannes W. Meijer_, Jul 06 2009