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%I #18 Feb 01 2024 08:19:07
%S 1,8,34,152,676,3008,13384,59552,264976,1179008,5245984,23341952,
%T 103859776,462123008,2056211584,9149092352,40708792576,181133355008,
%U 805951005184,3586070730752,15956184933376,70996881195008,315899894646784,1405593340977152,6254173153202176
%N a(n) = n!*[x^n] exp(2*x)*(y*sinh(x*y) + cosh(x*y)) and y = sqrt(6).
%H Colin Barker, <a href="/A335749/b335749.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,2).
%F a(n) = A335312(n, 6).
%F From _Colin Barker_, Jun 24 2020: (Start)
%F G.f.: (1 + 4*x) / (1 - 4*x - 2*x^2) for n>1.
%F a(n) = 4*a(n-1) + 2*a(n-2). (End)
%F a(n) = 4*A090017(n)+A090017(n+1). - _R. J. Mathar_, Mar 10 2022
%p aList := proc(len) local H; H := (x, y) -> exp(2*x)*(y*sinh(x*y) + cosh(x*y)):
%p series(H(x, sqrt(6)), x, len + 1): seq(k!*coeff(%, x, k), k=0..len-1) end:
%p aList(25);
%t LinearRecurrence[{4, 2}, {1, 8}, 30] (* _Paolo Xausa_, Feb 01 2024 *)
%o (PARI) Vec((1 + 4*x) / (1 - 4*x - 2*x^2) + O(x^25)) \\ _Colin Barker_, Jun 25 2020
%Y Cf. A335312.
%K nonn,easy
%O 0,2
%A _Peter Luschny_, Jun 24 2020
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