%I #24 Sep 08 2022 08:45:28
%S 8,75,463,2394,11274,50265,216581,912648,3788560,15565095,63484779,
%T 257591862,1041276566,4197718965,16888451857,67845945636,272258886492,
%U 1091657974275,4374492890615,17521540911570,70156842333538,280839342481425,1123993155149853
%N Expansion of g.f.: (8-29*x+24*x^2)/((1-4*x)*(1-3*x)*(1-2*x)^2*(1-x)^2).
%H G. C. Greubel, <a href="/A123003/b123003.txt">Table of n, a(n) for n = 0..1000</a>
%H E. Rodney Canfield and Herbert S. Wilf, <a href="https://arxiv.org/abs/math/0609704">Counting permutations by their runs up and down</a>, arXiv:math/0609704 [math.CO], 2006; See u_4.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (13,-67,175,-244,172,-48).
%F a(n) = (2*(n+1) + 1 - 16*(n-1)*2^n - 243*3^n + 64*4^(n+1))/4. - _Greg Dresden_, Jun 21 2021
%t LinearRecurrence[{13, -67, 175, -244, 172, -48}, {8, 75, 463, 2394, 11274, 50265}, 23] (* _Jean-François Alcover_, Oct 08 2018 *)
%o (Magma) [(2*n + 3 - (n-1)*2^(n+4) - 3^(n+5) + 4^(n+4))/4: n in [0..30]]; // _G. C. Greubel_, Jul 12 2021
%o (Sage) [(2*n + 3 - (n-1)*2^(n+4) - 3^(n+5) + 4^(n+4))/4 for n in [0..30]] # _G. C. Greubel_, Jul 12 2021
%Y Cf. A000352, A059427, A060158.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Nov 09 2006