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A005477 a(n) = 2^(n-1)*(2^n - 1)*Product_{j=1..n-1} (2^j + 1).

%I A005477 #16 Aug 18 2025 02:12:09
%S A005477 0,1,18,420,16200,1138320,152681760,40012315200,20727639504000,
%T A005477 21349793828563200,43852643645542617600,179883715700853141120000,
%U A005477 1474687052822610564537600000,24170122236238340825650936320000,792151597973733707815459821941760000,51919200227802645600849976559054284800000
%N A005477 a(n) = 2^(n-1)*(2^n - 1)*Product_{j=1..n-1} (2^j + 1).
%H A005477 G. C. Greubel, <a href="/A005477/b005477.txt">Table of n, a(n) for n = 0..75</a>
%F A005477 a(n) = 2^(n-2)*(2^n - 1)*QPochhammer(n, -1, 2). - _G. C. Greubel_, Nov 25 2022
%F A005477 a(n) ~ c * 2^((n^2+3*n-4)/2), where c = Product_{k>=0} (1 + 1/2^k) = A081845. - _Amiram Eldar_, Aug 18 2025
%p A005477 f := i->2^(i-1)*(2^i-1)*product( '2^j+1','j'=1..i-1);
%t A005477 Table[2^(n-1) (2^n-1)Product[2^j+1,{j,n-1}],{n,0,20}] (* _Harvey P. Dale_, Feb 02 2022 *)
%t A005477 Table[2^(n-2)*(2^n-1)*QPochhammer[-1,2,n], {n,0,30}] (* _G. C. Greubel_, Nov 25 2022 *)
%o A005477 (Magma) [n le 1 select n else 2^(n-1)*(2^n -1)*(&*[2^j+1: j in [1..n-1]]): n in [0..25]]; // _G. C. Greubel_, Nov 25 2022
%o A005477 (SageMath)
%o A005477 def A005477(n): return 2^(n-2)*(2^n-1)*product(2^j+1 for j in range(n))
%o A005477 [A005477(n) for n in range(30)] # _G. C. Greubel_, Nov 25 2022
%Y A005477 Cf. A081845.
%K A005477 nonn
%O A005477 0,3
%A A005477 _N. J. A. Sloane_
%E A005477 a(0) prepended by _G. C. Greubel_, Nov 25 2022