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%I #11 Feb 01 2024 08:18:43
%S 1,12,52,168,497,1412,3879,10360,27016,69024,173264,428288,1044480,
%T 2516992,6001408,14174208,33191936,77127680,177967104,408027136,
%U 930021376,2108424192,4756275200,10680270848,23880794112,53185871872,118016180224,260969594880,575223627776
%N Expansion of (1 + 4*x - 20*x^2 + 8*x^3 + 33*x^4 - 4*x^5 - 33*x^6)/(1 - 2*x)^4.
%H Paolo Xausa, <a href="/A339029/b339029.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F a(n) = 2^(n-7)*(588 + 367*n + 84*n^2 + 9*n^3) for n >= 3.
%p gf := (1 + 4*x - 20*x^2 + 8*x^3 + 33*x^4 - 4*x^5 - 33*x^6)/(1 - 2*x)^4:
%p ser := series(gf, x, 32): seq(coeff(ser, x, n), n = 0..28);
%t LinearRecurrence[{8, -24, 32, -16}, {1, 12, 52, 168, 497, 1412, 3879}, 30] (* _Paolo Xausa_, Feb 01 2024 *)
%Y Cf. A339252 (k=2), A339254 (k=3), A333650.
%K nonn
%O 0,2
%A _Peter Luschny_, Dec 01 2020