%I #11 Aug 21 2023 08:23:07

%S 1,1,-3,3,5,-22,27,28,-163,235,134,-1188,1983,408,-8504,16320,-1551,

%T -59659,131507,-46683,-408806,1040147,-612380,-2721835,8088003,

%U -6523626,-17457420,61883839,-62900496,-106248240,466069760,-571001695,-595520019,3454539427

%N G.f. satisfies A(x) = 1 + x*A(x) / (1 + x)^4.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-6,-4,-1).

%F G.f.: A(x) = 1/( 1 - x/(1+x)^4 ).

%F a(n) = -3*a(n-1) - 6*a(n-2) - 4*a(n-3) - a(n-4) for n > 4.

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n+3*k-1,n-k).

%t LinearRecurrence[{-3, -6, -4, -1}, {1, 1, -3, 3, 5}, 1 + 33] (* _Robert P. P. McKone_, Aug 21 2023 *)

%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n+3*k-1, n-k));

%Y Cf. A106510, A127896, A365084.

%Y Cf. A055991.

%K sign,easy

%O 0,3

%A _Seiichi Manyama_, Aug 21 2023