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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A275324 Expansion of (x*(1-4*x^2)^(-3/2) + (1-4*x^2)^(-1/2) + x + 1)/2. 2
1, 1, 1, 3, 3, 15, 10, 70, 35, 315, 126, 1386, 462, 6006, 1716, 25740, 6435, 109395, 24310, 461890, 92378, 1939938, 352716, 8112468, 1352078, 33801950, 5200300, 140408100, 20058300, 581690700, 77558760, 2404321560, 300540195, 9917826435, 1166803110, 40838108850 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..35.

FORMULA

Interweaved from (1+(1-4*x)^(-1/2))/2 (compare A088218 & A001700) and (1+(1-4*x)^(-3/2))/2 (compare A033876).

E.g.f.: (1 + x)*(1 + BesselI(0, 2*x))/2.

For a recurrence see the Sage script.

a(n) = A056040(n)/2 for n>=2.

MAPLE

st := (x*(1-4*x^2)^(-3/2)+(1-4*x^2)^(-1/2)+x+1)/2: series(st, x, 36):

PolynomialTools:-CoefficientList(convert(%, polynom), x);

MATHEMATICA

Table[If[n<2, 1, n!/Quotient[n, 2]!^2/2], {n, 0, 30}]

CoefficientList[Series[(x*(1 - 4*x^2)^(-3/2) + (1 - 4*x^2)^(-1/2) + x + 1)/2, {x, 0, 50}], x] (* G. C. Greubel, Aug 15 2016 *)

PROG

(Sage)

def A275324():

    r, n = 2, 1

    yield 1

    yield 1

    while True:

        n += 1

        r *= 4/n if is_even(n) else n

        yield r // 4

a = A275324(); print [a.next() for i in range(16)]

CROSSREFS

Cf. A001700, A033876, A088218, A056040.

Sequence in context: A285562 A285542 A160612 * A282663 A282124 A281421

Adjacent sequences:  A275321 A275322 A275323 * A275325 A275326 A275327

KEYWORD

nonn

AUTHOR

Peter Luschny, Aug 15 2016

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 July 17 21:36 EDT 2019. Contains 325109 sequences. (Running on oeis4.)