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A259877
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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)! ).
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2
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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
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OFFSET
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2,3
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LINKS
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FORMULA
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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
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MAPLE
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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)];
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MATHEMATICA
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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 *)
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PROG
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(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
for n in range(2, 10**2):
....a = 6*a//(n-1) if n % 2 else a*n*(n+1)//6
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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