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A104997
Denominators of coefficients in a series solution to a certain differential equation.
4
1, 8, 128, 15360, 3440640, 247726080, 653996851200, 476109707673600, 457065319366656000, 43034457761906688000, 850360885375276154880000, 1571466916173510334218240000, 693959790182222163590774784000, 9021477272368888126680072192000000, 27280947271643517695080538308608000000
OFFSET
1,2
COMMENTS
Series solution of o.d.e. (A. Gruzinov, 2005): cos(t)*f'(t) + sin(t)*f''(t) + (3/4)*sin(t)*f(t) = 0, f(-Pi/2) = 1, f'(-Pi/2) = 0, f(t) = 1 - (3/8)*(t + Pi/2)^2 - (5/128)*(t + Pi/2)^4 - (193/15360)*(t + Pi/2)^4 - ... All coefficients (except 1) are negative, there is no simple recursion or other formula for the series coefficients.
LINKS
Andrei Gruzinov, Power of an axisymmetric pulsar, Physical Review Letters, Vol. 94, No. 2 (2005), 021101; arXiv preprint, arXiv:astro-ph/0407279, 2004.
FORMULA
The solution to the o.d.e. is hypergeom([-1/4,3/4],[1/2],sin(t+Pi/2)). - Robert Israel, Jun 05 2019
MAPLE
de:= sin(s)*D(g)(s)-cos(s)*(D@@2)(g)(s)-3/4*cos(s)*g(s)=0:
S:= dsolve({de, g(0)=1, D(g)(0)=0}, g(s), series, order=51):
seq(denom(coeff(rhs(S), s, 2*j)), j=0..25); # Robert Israel, Jun 05 2019
MATHEMATICA
CoefficientList[Series[Hypergeometric2F1[-1/4, 3/4, 1/2, Sin[x]^2], {x, 0, 30}], x][[1 ;; -1 ;; 2]] // Denominator (* Amiram Eldar, Apr 29 2023 *)
CROSSREFS
Cf. A104996 (numerators).
Sequence in context: A219264 A349263 A188060 * A265097 A027951 A041115
KEYWORD
nonn,frac
AUTHOR
Zak Seidov, Mar 31 2005
EXTENSIONS
More terms from Robert Israel, Jun 05 2019
STATUS
approved