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A009120 a(n) = (4n)!/(2n)!. 2
1, 12, 1680, 665280, 518918400, 670442572800, 1295295050649600, 3497296636753920000, 12576278705767096320000, 58102407620643984998400000, 335367096786357081410764800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Absolute value of the coefficients in the expansion of cos(x^2). - clarified by Muniru A Asiru, Jul 26 2018

Bisection of sequence A001813. - Gary W. Adamson, Jul 19 2011

Expansion of cosh(x^2) in powers of x^4. - G. C. Greubel, Jul 26 2018

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

FORMULA

a(n) = 4^n * A101485(n).

Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int((1/4)*exp(-1/4*sqrt(x))/(sqrt(Pi)*x^(3/4)), x=0..infinity), n=0, 1... - Karol A. Penson, Sep 19 2001

From Gary W. Adamson, Jul 19 2011: (Start)

a(n) = upper left term of M^(2n), where M = an infinite square production matrix as follows:

  2, 2, 0, 0, 0, 0, ...

  4, 4, 4, 0, 0, 0, ...

  6, 6, 6, 6, 0, 0, ...

  8, 8, 8, 8, 8, 0, ...

  ... (End)

MAPLE

seq(coeff(series(factorial(n)*cosh(x^2), x, n+1), x, n), n=0..50, 4); # Muniru A Asiru, Jul 27 2018

MATHEMATICA

Table[(4n)!/(2n)!, {n, 0, 10}] (* or *) With[{nn=60}, Abs[Take[ CoefficientList[ Series[ Cos[x^2], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 4}]]] (* Harvey P. Dale, Mar 27 2012 *)

PROG

(MAGMA) [Factorial(4*n)/Factorial(2*n): n in [0..15]]; // Vincenzo Librandi, Jul 20 2011

(PARI) for(n=0, 20, print1((4*n)!/(2*n)!, ", ")) \\ G. C. Greubel, Jul 26 2018

(PARI) x='x+O('x^120); v=Vec(serlaplace(cosh(x^2))); vector(#v\4, n, v[4*n-3]) \\ G. C. Greubel, Jul 26 2018

(GAP) List([0..25], n->Factorial(4*n)/Factorial(2*n)); # Muniru A Asiru, Jul 26 2018

CROSSREFS

Cf. A001813, A101485.

Sequence in context: A271436 A034280 A146201 * A078928 A202968 A013717

Adjacent sequences:  A009117 A009118 A009119 * A009121 A009122 A009123

KEYWORD

nonn,easy

AUTHOR

R. H. Hardin

EXTENSIONS

Extended by Olivier Gérard, Mar 01 1997

STATUS

approved

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Last modified October 18 11:56 EDT 2018. Contains 316321 sequences. (Running on oeis4.)