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A271385 a(n) = Product_{k=0..floor((n - 1)/2)} (n - 2*k)^(n - 2*k). 1

%I

%S 1,1,4,27,1024,84375,47775744,69486440625,801543976648704,

%T 26920470805806965625,8015439766487040000000000,

%U 7680724499239438722449399746875,71466466094944065310414602240000000000,2326300251412874049290421829657963142035959375

%N a(n) = Product_{k=0..floor((n - 1)/2)} (n - 2*k)^(n - 2*k).

%C Double hyperfactorial (by analogy with the double factorial).

%H Ilya Gutkovskiy, <a href="/A271385/b271385.txt">Table of n, a(n) for n = 0..33</a>

%H Ilya Gutkovskiy, <a href="/A271385/a271385.pdf">Double hyperfactorial</a>

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/DoubleFactorial.html">Double Factorial</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hyperfactorial.html">Hyperfactorial</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%F a(n) = n^n*(n - 2)^(n - 2)*...*5^5*3^3*1^1, for n>0 odd; a(n) = n^n*(n - 2)^(n - 2)*...*6^6*4^4*2^2, for n>0 even; a(n) = 1, for n = 0.

%F a(n) = n^n*a(n-2), a(0)=1, a(1)=1.

%F a(n) = (1/a(n-1))*sqrt(a(2n)/2^(n*(n+1))).

%F a(n)*a(n-1) = A002109(n).

%F a(n)*a(n-1)*sqrt(a(2n))/((n!)^n*sqrt(2^(n*(n+1)))) = A168510(n).

%e a(0) = 1;

%e a(1) = 1^1 = 1;

%e a(2) = 2^2 = 4;

%e a(3) = 1^1*3^3 = 27;

%e a(4) = 2^2*4^4 = 1024;

%e a(5) = 1^1*3^3*5^5 = 84375;

%e a(6) = 2^2*4^4*6^6 = 47775744;

%e a(7) = 1^1*3^3*5^5*7^7 = 69486440625;

%e a(8) = 2^2*4^4*6^6*8^8 = 801543976648704, etc.

%t Table[Product[(n - 2 k)^(n - 2 k), {k, 0, Floor[(n - 1)/2]}], {n, 0, 13}]

%t RecurrenceTable[{a[0] == 1, a[1] == 1, a[n] == n^n a[n - 2]}, a, {n, 13}]

%o (PARI) a(n) = prod(k=0, (n-1)\2, (n-2*k)^(n-2*k)); \\ _Michel Marcus_, Apr 07 2016

%Y Cf. A002109, A006882, A168510.

%K nonn,easy

%O 0,3

%A _Ilya Gutkovskiy_, Apr 06 2016

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Last modified October 20 01:39 EDT 2018. Contains 316378 sequences. (Running on oeis4.)