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A104997 Denominators of coefficients in a series solution to a certain ODE. 4
1, 8, 128, 15360, 3440640, 247726080, 653996851200, 476109707673600, 457065319366656000, 43034457761906688000, 850360885375276154880000, 1571466916173510334218240000, 693959790182222163590774784000, 9021477272368888126680072192000000, 27280947271643517695080538308608000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Series solution of ode (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.

REFERENCES

A. Gruzinov, Power of axisymmetric pulsar, Phys. Rev. Lett. 94 (021101)(2005).

LINKS

Robert Israel, Table of n, a(n) for n = 1..203

A. Gruzinov, Power of axisymmetric pulsar, arXiv:astro-ph/0407279, 2004.

FORMULA

The solution to the ode 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

CROSSREFS

Cf. A104996 (numerators).

Sequence in context: A113135 A219264 A188060 * A265097 A027951 A041115

Adjacent sequences:  A104994 A104995 A104996 * A104998 A104999 A105000

KEYWORD

nonn,frac

AUTHOR

Zak Seidov, Mar 31 2005

EXTENSIONS

More terms from Robert Israel, Jun 05 2019

STATUS

approved

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Last modified October 21 11:42 EDT 2019. Contains 328296 sequences. (Running on oeis4.)