%I #18 Aug 09 2024 18:14:40

%S 1,1,2,8,56,448,4928,64064,896896,14350336,272656384,5725784064,

%T 125967249408,3149181235200,81878712115200,2292603939225600,

%U 71070722115993600,2274263107711795200,79599208769912832000,2945170724486774784000,111916487530497441792000,4588575988750395113472000

%N Partial products of odious numbers.

%H Harvey P. Dale, <a href="/A308501/b308501.txt">Table of n, a(n) for n = 0..404</a>

%H J.-P. Allouche, <a href="https://arxiv.org/abs/1906.10532">The zeta-regularized product of odious numbers</a>, arXiv:1906.10532 [math.NT], 2019.

%F a(n) = Product_{k=1..n} A000069(k).

%t Join[{1},FoldList[Times,Select[Range[0,50],OddQ[DigitCount[#,2,1]]&]]] (* _Harvey P. Dale_, Aug 09 2024 *)

%o (PARI) f(n) = 2*n - 1 - hammingweight(n-1)%2; \\ A000069

%o a(n) = prod(k=1, n, f(k))

%Y Cf. A000069 (odious numbers).

%K nonn

%O 0,3

%A _Michel Marcus_, Jun 26 2019