login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A032427 Coefficients of Jacobi elliptic function c(4,m). 0
1, 11069, 4494351, 834687179, 109645021894, 11966116940238, 1171517154238290, 107266611330420090, 9412382749388124015, 803475280086029066515, 67362921649153881472361, 5581153512072331417781229 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. Fransen, Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function sn(n,k), Math. Comp., 37 (1981), 475-497.

LINKS

Table of n, a(n) for n=0..11.

A. Fransen, Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function sn(n,k), Math. Comp., 37 (1981), 475-497.

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]

FORMULA

a(n) = (3^(4*n+19) - (24*n+36)*7^(2*n+9) + (96*n^2+312*n+150)*5^(2*n+9) - (256*n^3+1344*n^2+1520*n+117)*3^(2*n+9) + 512*n^4+3584*n^3+6208*n^2+1336*n-846) / 196608. - Vaclav Kotesovec after Fransen, Jul 30 2013

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); # Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010

CROSSREFS

Sequence in context: A139409 A233789 A236151 * A204758 A211686 A224463

Adjacent sequences:  A032424 A032425 A032426 * A032428 A032429 A032430

KEYWORD

nonn

AUTHOR

Simon Plouffe

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 02:29 EDT 2021. Contains 348141 sequences. (Running on oeis4.)