login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259877 If n is even then a(n) = n!/( 2^(n/2)*(n/2)! ), otherwise a(n) = n!/( 3*2^((n-1)/2)*((n-3)/2)! ). 2
1, 1, 3, 10, 15, 105, 105, 1260, 945, 17325, 10395, 270270, 135135, 4729725, 2027025, 91891800, 34459425, 1964187225, 654729075, 45831035250, 13749310575, 1159525191825, 316234143225, 31623414322500, 7905853580625, 924984868933125, 213458046676875, 28887988983603750, 6190283353629375 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Chai Wah Wu, Table of n, a(n) for n = 2..501

D. L. Andrews, Letter to N. J. A. Sloane, Apr 10 1978.

D. L. Andrews and T. Thirunamachandran, On three-dimensional rotational averages, J. Chem. Phys., 67 (1977), 5026-5033. See N_n.

D. L. Andrews and T. Thirunamachandran, On three-dimensional rotational averages, J. Chem. Phys., 67 (1977), 5026-5033. [Annotated scanned copy]

FORMULA

a(n) = (n!/6)*2^(-n/2)*(((2^(1/2)*(1-(-1)^n))/(n/2-3/2)!)+3*(1+(-1)^n)/(n/2)!). - Wesley Ivan Hurt, Jul 10 2015

a(n+1) = a(n)*n*(n+1)/6 if n is even, a(n+1) = 6*a(n)/(n-1) if n is odd. - Chai Wah Wu, Jul 15 2015

a(2*n) = A001147(n), a(2*n+1) = A000457(n-1). - Yuchun Ji, Nov 02 2020

MAPLE

f:=proc(n) if n mod 2 = 0 then

n!/(2^(n/2)*(n/2)!) else

n!/( 3*2^((n-1)/2)*((n-3)/2)! ); fi; end;

[seq(f(n), n=2..30)];

MATHEMATICA

Table[(n!/6)*2^(-n/2)*(((2^(1/2)*(1-(-1)^n))/(n/2-3/2)!)+3*(1+(-1)^n)/(n/2)!), {n, 2, 30}] (* Wesley Ivan Hurt, Jul 10 2015 *)

PROG

(PARI) main(size)={v=vector(size); for(n=2, size+1, if(n%2==0, v[n-1]=n!/(2^(n/2)*(n/2)!), v[n-1]=n!/( 3*2^((n-1)/2)*((n-3)/2)!))); return(v); } /* Anders Hellström, Jul 10 2015 */

(Python)

from __future__ import division

A259877_list, a = [1], 1

for n in range(2, 10**2):

....a = 6*a//(n-1) if n % 2 else a*n*(n+1)//6

....A259877_list.append(a) # Chai Wah Wu, Jul 15 2015

CROSSREFS

A001147 alternating with A000457. Interlaced diagonal of A008299.

Sequence in context: A037345 A217278 A175336 * A182334 A051420 A092827

Adjacent sequences:  A259874 A259875 A259876 * A259878 A259879 A259880

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 09 2015

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 December 6 13:45 EST 2021. Contains 349563 sequences. (Running on oeis4.)