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A104996
Numerators of coefficients in a series solution to a certain differential equation.
3
1, -3, -5, -193, -13397, -315629, -282682949, -71668311457, -24436072994261, -829687356768133, -5984214162917084933, -4076572731127688098561, -669050282555409820416913, -3254803666762108782733299553, -3704926048371364507765541554757, -975581171350361622823383714646061
OFFSET
1,2
COMMENTS
Serial 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 for 1) are negative, and there is no simple recursion or other formula for the serial 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.
MATHEMATICA
CoefficientList[Series[Hypergeometric2F1[-1/4, 3/4, 1/2, Sin[x]^2], {x, 0, 30}], x][[1 ;; -1 ;; 2]] // Numerator (* Amiram Eldar, Apr 29 2023 *)
CROSSREFS
Cf. A104997 (denominators).
Sequence in context: A092947 A337158 A333413 * A211767 A224537 A175133
KEYWORD
sign,frac
AUTHOR
Zak Seidov, Mar 31 2005
EXTENSIONS
More terms from Amiram Eldar, Apr 29 2023
STATUS
approved