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%I #15 May 06 2022 07:33:14
%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.
%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 *)
%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
%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.
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