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 A162444 Denominators of the BG1[ -5,n] coefficients of the BG1 matrix 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 14 23:14 EDT 2024. Contains 375171 sequences. (Running on oeis4.)