login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123687 E.g.f.: (1-x^2)^(-1/2)*exp(x^2/(1-x^2))*BesselI(0,x^2/(x^2-1)) (since this is an even function, we do not give the intercalating 0's). 1
1, 3, 63, 3225, 297675, 42805665, 8790957945, 2433297161295, 870928551367875, 390718610250593625, 214426984078881899325, 141173178618822867992475, 109729771971447612972712725, 99352716603692210781106359375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..221

FORMULA

(n+1)*(2*n+3)^2*(2*n+1)^2*a(n) - (2*n+5)*(2*n+3)^2*a(n+1) + (n+2)*a(n+2) = 0. - Robert Israel, Oct 10 2016

a(n) ~ 2^(2*n - 1/4) * exp(2*sqrt(2*n) - 2*n - 1) * n^(2*n - 1/4) / sqrt(Pi) * (1 + 67/(48*sqrt(2*n))). - Vaclav Kotesovec, Nov 13 2017

MAPLE

G:=(1-x^2)^(-1/2)*exp(x^2/(1-x^2))*BesselI(0, x^2/(x^2-1)): Gser:=series(G, x=0, 40): seq((2*n)!*coeff(Gser, x, 2*n), n=0..15); # Emeric Deutsch, Oct 31 2006

MATHEMATICA

DeleteCases[Flatten@ MapIndexed[#1 (#2 - 1)! &, CoefficientList[Series[(1 - x^2)^(-1/2) Exp[x^2/(1 - x^2)] BesselI[0, x^2/(x^2 - 1)], {x, 0, 26}], x]], 0] (* Michael De Vlieger, Oct 10 2016 *)

With[{nmax = 50}, CoefficientList[Series[(1 - x^2)^(-1/2)*Exp[x^2/(1 - x^2)]*BesselI[0, x^2/(x^2 - 1)], {x, 0, nmax}], x]*Range[0, nmax]!][[;; ;; 2 ]] (* G. C. Greubel, Oct 18 2017 *)

CROSSREFS

Cf. A123510, A123511, A123512, A123525, A123686.

Sequence in context: A139293 A133275 A258657 * A159605 A180761 A156904

Adjacent sequences:  A123684 A123685 A123686 * A123688 A123689 A123690

KEYWORD

nonn

AUTHOR

Karol A. Penson, Oct 06 2006

EXTENSIONS

More terms from Emeric Deutsch, Oct 31 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 23 20:23 EDT 2019. Contains 323528 sequences. (Running on oeis4.)