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Search: id:A162444
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| A162444 |
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Denominators of the BG1[ -5,n] coefficients of the BG1 matrix |
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+0
2
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| 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
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OFFSET
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1,3
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COMMENT
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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).
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FORMULA
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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)!.
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EXAMPLE
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The first few formulae 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)!
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CROSSREFS
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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: A109173 A103010 A068111 this_sequence A052468 A055786 A001790
Adjacent sequences: A162441 A162442 A162443 this_sequence A162445 A162446 A162447
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009
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