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Last term in n-th row of A080508.
3

%I #18 Nov 06 2018 13:20:48

%S 1,4,4,216,324,6075000,30375000,750453558750000,19699405917187500,

%T 459652804734375000,9652708899421875000,

%U 578346405423301688948883281250000,111331683043985575122660031640625000,77892265302487151682927242578030755976166730468750000

%N Last term in n-th row of A080508.

%H Jeppe Stig Nielsen, <a href="/A080509/b080509.txt">Table of n, a(n) for n = 1..54</a>

%F For n!=2, a(n) = (A034386(n - 1))^n / (n - 1)!. - _Jeppe Stig Nielsen_, Nov 04 2018

%e For n=5, first four terms of row are 1, 2, 3, 4, with product 24 = 2^3*3^1. So last term is 2^(5-3)*3^(5-1) = 2^2*3^4 = 324.

%t MapAt[4 # &, Array[Apply[Times, Prime@ Range@ PrimePi[# - 1]]^#/(# - 1)! &, 14], 2] (* _Michael De Vlieger_, Nov 05 2018 *)

%o (PARI) a(n) = {if (n == 1, return (1)); if (n == 2, return (2^2)); f = factor((n-1)!); prod(i = 1, #f~, f[i,1]^(n - f[i,2]));} \\ _Michel Marcus_, Aug 30 2013

%o (PARI) a(n) = if(n==2, 4, prod(i=1,primepi(n-1),prime(i))^n/(n-1)!) \\ _Jeppe Stig Nielsen_, Nov 04 2018

%Y Cf. A080508.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Mar 20 2003

%E More terms from _Michel Marcus_, Aug 30 2013