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A298595 G.f.: Sum_{n>=0} a(n)*x^(2*n)/((2*n)!)^2 = 1/BesselJ(0,x). 0
1, 1, 27, 4275, 2326275, 3260434275, 9824561849025, 56272951734424425, 560476093710119461875, 9074718916938795106861875, 226586114542199918676706160625, 8362768986063791790897266120885625, 440616849129306857329147873116900455625, 32189976281042425371050387695609814928515625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..13.

Index entries for sequences related to Bessel functions or polynomials

FORMULA

a(n) = ((2*n)!)^2 * [x^(2*n)] 1/BesselJ(0,x).

EXAMPLE

1/BesselJ(0,x) = 1 + x^2/(2!)^2 + 27*x^4/(4!)^2 + 4275*x^6/(6!)^2 + 2326275*x^8/(8!)^2 + ...

MATHEMATICA

nmax = 13; Table[(CoefficientList[Series[1/BesselJ[0, x], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!^2)[[n]], {n, 1, 2 nmax + 1, 2}]

nmax = 13; Table[(CoefficientList[Series[1/Hypergeometric0F1[1, -x^2/4], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!^2)[[n]], {n, 1, 2 nmax + 1, 2}]

CROSSREFS

Cf. A000275, A001818, A002454.

Sequence in context: A271240 A223327 A211927 * A278686 A046367 A059795

Adjacent sequences:  A298592 A298593 A298594 * A298596 A298597 A298598

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 22 2018

STATUS

approved

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Last modified July 29 14:59 EDT 2021. Contains 346346 sequences. (Running on oeis4.)