OFFSET
1,1
LINKS
Harry J. Smith, Table of n, a(n) for n=1..100
FORMULA
a(n) = Product_{k=1..n} (n^2 - n + 2*k) = (n^2 + n)!!/(n^2 - n)!! .
a(n) = 2^n*Gamma((n^2 + n + 2)/2)/Gamma(n^2 - n + 2)/2).
a(n) = 2^n * A057003(n-1).
EXAMPLE
a(3) = 8*10*12 = 960.
MATHEMATICA
Table[2^n*Gamma[(2+n+n^2)/2]/Gamma[(2-n+n^2)/2], {n, 30}] (* G. C. Greubel, May 05 2022 *)
With[{nn=30}, Times@@@TakeList[Range[2, (nn(nn+1))/2, 2], Range[nn/2]]] (* Harvey P. Dale, May 09 2022 *)
PROG
(PARI) { for (n=1, 60, write("b062029.txt", n, " ", 2^n*((n^2 + n)/2)!/((n^2 - n)/2)!) ) } \\ Harry J. Smith, Jul 30 2009
(SageMath) [2^n*gamma((2+n+n^2)/2)/gamma((2-n+n^2)/2) for n in (1..30)] # G. C. Greubel, May 05 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jun 02 2001
EXTENSIONS
Formula and more terms from Vladeta Jovovic, Jun 05 2001
STATUS
approved