cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A062030 Group even numbers into (2,4), (6,8,10,12), (14,16,18,20,22,24), ...; a(n) = product of n-th group.

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%I A062030 #27 Jun 09 2025 12:16:43
%S A062030 8,5760,42577920,1300252262400,111644006842368000,
%T A062030 21695920874860629196800,8291067715225260172247040000,
%U A062030 5644260808699395278689265516544000,6360332664265371581768550654463180800000,11209384544297234954537967755979151481241600000,29531169256166572959626706182319305835700813824000000
%N A062030 Group even numbers into (2,4), (6,8,10,12), (14,16,18,20,22,24), ...; a(n) = product of n-th group.
%C A062030 a(113) has 997 digits and a(114) has 1007 digits. - _Harvey P. Dale_, Nov 24 2024
%H A062030 Harry J. Smith, <a href="/A062030/b062030.txt">Table of n, a(n) for n=1..100</a>
%F A062030 a(n) = 4^n * Gamma(1 + n + n^2)/Gamma(1 - n + n^2). - _G. C. Greubel_, May 06 2022
%F A062030 a(n) ~ 4^n * n^(4*n). - _Vaclav Kotesovec_, Jun 09 2025
%e A062030 a(3) = 14*16*18*20*22*24 = 42577920.
%t A062030 Table[4^n*Gamma[1+n+n^2]/Gamma[1-n+n^2], {n,30}] (* _G. C. Greubel_, May 05 2022 *)
%t A062030 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 A062030 (PARI) a(n) = { 2^(2*n)*(n^2+n)!/(n^2-n)! } \\ _Harry J. Smith_, Jul 30 2009
%o A062030 (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 A062030 Cf. A062029, A062031, A062032.
%K A062030 nonn
%O A062030 1,1
%A A062030 _Amarnath Murthy_, Jun 02 2001
%E A062030 More terms from _Jason Earls_, Jun 10 2001
%E A062030 Typo in a(4) corrected by _N. J. A. Sloane_, Aug 31 2009 using the b-file.