%I #9 Feb 06 2024 10:17:23

%S 1,9,48,204,765,2649,8680,27312,83313,247985,723624,2077164,5880797,

%T 16454865,45577200,125130432,340882113,922265721,2479938368,

%U 6631802220,17646603933,46744464745,123314065944,324085913136,848801213425

%N A001333(n), n >= 1, convolved twice with itself.

%C a(n) = A054458(n+2,2) (third column of convolution triangle).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,-4,9,6,1)

%F a(n) = (n+1)*(LP2(n+1)+2*LP2(n)+LP2(n-1))/8, n >= 1, LP2(n) = A054459(n), a(0) = 1.

%F a(n) = (n+1)*((10*n+11)*LP(n)+(4*n+5)*LP(n-1))/16, n >= 1, LP(n) = A001333(n+1).

%F G.f.: ((1+x)/(1-2*x-x^2))^3.

%F a(n) = +6*a(n-1) -9*a(n-2) -4*a(n-3) +9*a(n-4) +6*a(n-5) +a(n-6). - _R. J. Mathar_, Feb 05 2024

%t LinearRecurrence[{6, -9, -4, 9, 6, 1}, {1, 9, 48, 204, 765, 2649}, 30] (* _Paolo Xausa_, Feb 06 2024 *)

%Y Cf. A054458, A054459, A001333, A002203.

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_, Apr 26 2000