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A032427
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Coefficients of Jacobi elliptic function c(4,m).
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0
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1, 11069, 4494351, 834687179, 109645021894, 11966116940238, 1171517154238290, 107266611330420090, 9412382749388124015, 803475280086029066515, 67362921649153881472361, 5581153512072331417781229
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| A. Fransen, Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function sn(n,k), Math. Comp., 37 (1981), 475-497.
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LINKS
| S. Wrigge, Calculation of the Taylor series expansion coefficients of the Jacobian elliptic function sn(x, k), Math. Comp. 36 (1981), 555-564. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010]
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MAPLE
| a:=proc(n) options remember: local m: if n>2 then if n mod 2 = 0 then m:=n/2-1: RETURN(-4*(1+k^2)*a(n-2)+6*k^2*add(binomial(n-2, 2*v)*a(2*v)*a(n-2-2*v), v=1..m-1)) else m:=(n-1)/2-1: RETURN(-(1+k^2)*a(n-2)+2*k^2*add(binomial(n-2, 2*v+1)*a(2*v+1)*a(n-3-2*v), v=0..m-1)) fi else RETURN([1, 2][n]) fi:end: seq(abs(coeff(a(2*i+1), k, 8)), i=4..23); [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010]
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CROSSREFS
| Sequence in context: A164518 A198208 A139409 * A204758 A204226 A158619
Adjacent sequences: A032424 A032425 A032426 * A032428 A032429 A032430
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com).
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EXTENSIONS
| More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010
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