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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A009564 E.g.f. sin(x^2)/2, coefficients of x^(4*n + 2). 3
1, -60, 15120, -8648640, 8821612800, -14079294028800, 32382376266240000, -101421602465863680000, 415017197290314178560000, -2149789081963827444940800000, 13750050968240640337841356800000, -106425394494182556214892101632000000, 980390734080409707851586040233984000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..182

FORMULA

a(n) = (-1)^n*(2+4*n)!/(2*(1+2*n)!) = (-1)^n*A001813(2*n+1)/2. - Robert Israel, Dec 21 2015

MAPLE

seq(i!*coeff(series(sin(x^2)/2, x, 4*i+4), x, i), i=2..54, 4); # Peter Luschny, Dec 14 2012

MATHEMATICA

nmax = 12; coes = CoefficientList[ Series[ Sin[x^2]/2, {x, 0, 4*nmax + 2}], x]; a[n_] := coes[[4*n + 3]]*(4*n + 2)!; Table[a[n], {n, 0, nmax}] (* Jean-Fran├žois Alcover, Dec 14 2012 *)

Table[(-1)^n (2 + 4 n)!/(2 (1 + 2 n)!), {n, 0, 25}] (* Vincenzo Librandi, Dec 22 2015 *)

PROG

(Sage)

def A009564(n):

    return falling_factorial(4*n+2, 2*n+1)/(2*(-1)^n)

[A009564(n) for n in (0..12)]  # Peter Luschny, Dec 14 2012

(MAGMA) [(-1)^n*Factorial(2+4*n)/(2*Factorial(1+2*n)): n in [0..20]]; // Vincenzo Librandi, Dec 22 2015

(PARI) a(n) = (-1)^n*(2+4*n)!/(2*(1+2*n)!); \\ Altug Alkan, Dec 22 2015

CROSSREFS

Cf. A001813, A103639, A024343, A075069.

Sequence in context: A184890 A295598 A113424 * A269762 A291912 A001460

Adjacent sequences:  A009561 A009562 A009563 * A009565 A009566 A009567

KEYWORD

sign

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs Mar 1997

Definition corrected and terms a(10)-a(12) from Peter Luschny, Dec 14 2012

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 06:25 EDT 2018. Contains 316405 sequences. (Running on oeis4.)