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%I #13 Aug 06 2018 05:34:31
%S 1,4,16,64,280,1504,9856,70144,498136,3449440,23506816,160566784,
%T 1115048896,7905796864,56994288640,414928113664,3034880623576,
%U 22255957312864,163667338903936,1208070406612480,8955840250934080,66678657938510080
%N a(n) = 4^n*hypergeom([-n/4, (1-n)/4, (2-n)/4, (3-n)/4], [1, 1, 1], 1).
%C Diagonal of rational function 1/(1 - (x^4 + y^4 + z^4 + t^4 + 4*x*y*z*t)). - _Gheorghe Coserea_, Aug 04 2018
%F Let H(m, n, x) = m^n*hypergeom([(k-n)/m for k=0..m-1], [1 for k=0..m-2], x) then a(n) = H(4, n, 1).
%F a(n) ~ 2^(3*n + 2) / (Pi*n)^(3/2). - _Vaclav Kotesovec_, Nov 02 2017
%p T := (m,n,x) -> m^n*hypergeom([seq((k-n)/m, k=0..m-1)], [seq(1, k=0..m-2)], x):
%p lprint(seq(simplify(T(4,n,1)), n=0..39));
%t Table[4^n * HypergeometricPFQ[{-n/4, (1-n)/4, (2-n)/4, (3-n)/4}, {1, 1, 1}, 1], {n, 0, 30}] (* _Vaclav Kotesovec_, Nov 02 2017 *)
%Y H(1, n, 1) = A000007(n), H(2, n, 1) = A000984(n), H(3, n, 1) = A006077(n), H(4, n, 1) = this seq., H(1, n, -1) = A000079(n), H(2, n, -1) = A098335(n), H(3, n, -1) = A294035(n), H(4, n, -1) = A294037(n).
%K nonn
%O 0,2
%A _Peter Luschny_, Nov 02 2017