login
Group even numbers into (2,4), (6,8,10,12), (14,16,18,20,22,24), ...; a(n) = product of n-th group.
5

%I #23 Nov 24 2024 11:37:11

%S 8,5760,42577920,1300252262400,111644006842368000,

%T 21695920874860629196800,8291067715225260172247040000,

%U 5644260808699395278689265516544000,6360332664265371581768550654463180800000,11209384544297234954537967755979151481241600000,29531169256166572959626706182319305835700813824000000

%N Group even numbers into (2,4), (6,8,10,12), (14,16,18,20,22,24), ...; a(n) = product of n-th group.

%C a(113) has 997 digits and a(114) has 1007 digits. - _Harvey P. Dale_, Nov 24 2024

%H Harry J. Smith, <a href="/A062030/b062030.txt">Table of n, a(n) for n=1..100</a>

%F a(n) = 4^n * Gamma(1 + n + n^2)/Gamma(1 - n + n^2). - _G. C. Greubel_, May 06 2022

%e a(3) = 14*16*18*20*22*24 = 42577920.

%t Table[4^n*Gamma[1+n+n^2]/Gamma[1-n+n^2], {n,30}] (* _G. C. Greubel_, May 05 2022 *)

%t Module[{nn=20,ev,l},ev=2*Range[nn(nn+1)];l=2*Range[nn];Times@@@TakeList[ev,l]] (* _Harvey P. Dale_, Nov 24 2024 *)

%o (PARI) { for(n=1, 100, write("b062030.txt", n, " ", 2^(2*n)*(n^2+n)!/(n^2-n)!) ) } \\ _Harry J. Smith_, Jul 30 2009

%o (SageMath) [4^n*gamma(1+n+n^2)/gamma(1-n+n^2) for n in (1..30)] # _G. C. Greubel_, May 05 2022

%Y Cf. A062029, A062031, A062032.

%K nonn,changed

%O 1,1

%A _Amarnath Murthy_, Jun 02 2001

%E More terms from _Jason Earls_, Jun 10 2001

%E Typo in a(4) corrected by _N. J. A. Sloane_, Aug 31 2009 using the b-file.