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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)