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a(n) = ((2n-1)!!)^4 * Sum_{i=1..n} 1/(2*i-1)^4.
4

%I #13 Sep 02 2017 12:22:33

%S 0,1,82,51331,123296356,809068942341,11846375878465206,

%T 338356017569383549191,17129606870671774862445000,

%U 1430698777932227525446706735625,186451505481090040331197201556276250,36261458995575361475673937929555130516875

%N a(n) = ((2n-1)!!)^4 * Sum_{i=1..n} 1/(2*i-1)^4.

%H Seiichi Manyama, <a href="/A291586/b291586.txt">Table of n, a(n) for n = 0..126</a>

%F a(0) = 0, a(1) = 1, a(n+1) = ((2*n-1)^4+(2*n+1)^4)*a(n) - (2*n-1)^8*a(n-1) for n > 0.

%F a(n) ~ Pi^4 * 2^(4*n-3) * n^(4*n) / (3*exp(4*n)). - _Vaclav Kotesovec_, Aug 27 2017

%t Table[(2*n-1)!!^4 * Sum[1/(2*i-1)^4, {i, 1, n}], {n, 0, 15}] (* _Vaclav Kotesovec_, Aug 27 2017 *)

%Y Cf. A001147, A203229.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 27 2017