cp's OEIS Frontend

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)! ).

%I A259877 #33 May 22 2025 10:21:43
%S A259877 1,1,3,10,15,105,105,1260,945,17325,10395,270270,135135,4729725,
%T A259877 2027025,91891800,34459425,1964187225,654729075,45831035250,
%U A259877 13749310575,1159525191825,316234143225,31623414322500,7905853580625,924984868933125,213458046676875,28887988983603750,6190283353629375
%N 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)! ).
%H A259877 Chai Wah Wu, <a href="/A259877/b259877.txt">Table of n, a(n) for n = 2..501</a>
%H A259877 D. L. Andrews, <a href="/A005043/a005043.pdf">Letter to N. J. A. Sloane</a>, Apr 10 1978.
%H A259877 D. L. Andrews and T. Thirunamachandran, <a href="http://dx.doi.org/10.1063/1.434725">On three-dimensional rotational averages</a>, J. Chem. Phys., 67 (1977), 5026-5033. See N_n.
%H A259877 D. L. Andrews and T. Thirunamachandran, <a href="/A005043/a005043_1.pdf">On three-dimensional rotational averages</a>, J. Chem. Phys., 67 (1977), 5026-5033. [Annotated scanned copy]
%F A259877 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
%F A259877 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
%F A259877 a(2*n) = A001147(n), a(2*n+1) = A000457(n-1). - _Yuchun Ji_, Nov 02 2020
%p A259877 f:=proc(n) if n mod 2 = 0 then
%p A259877 n!/(2^(n/2)*(n/2)!) else
%p A259877 n!/( 3*2^((n-1)/2)*((n-3)/2)! ); fi; end;
%p A259877 [seq(f(n),n=2..30)];
%t A259877 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 *)
%o A259877 (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 */
%o A259877 (Python)
%o A259877 from __future__ import division
%o A259877 A259877_list, a = [1], 1
%o A259877 for n in range(2,10**2):
%o A259877     a = 6*a//(n-1) if n % 2 else a*n*(n+1)//6
%o A259877     A259877_list.append(a) # _Chai Wah Wu_, Jul 15 2015
%Y A259877 A001147 alternating with A000457. Interlaced diagonal of A008299.
%K A259877 nonn
%O A259877 2,3
%A A259877 _N. J. A. Sloane_, Jul 09 2015