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%I #7 Apr 08 2021 03:49:38
%S 1,15,110,545,2120,7043,20965,57560,148545,365045,862224,1970905,
%T 4382820,9520315,20265665,42385132,87284120,177293730,355738710,
%U 705980760,1387213926,2701362950,5217448800,10001654350
%N Fourth convolution of Lucas numbers A000032(n+1), n >= 0.
%H G. C. Greubel, <a href="/A060931/b060931.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-10,15,11,-15,-10,5,5,1).
%F a(n) = A060921(n+4, 4) (fifth column of Lucas triangle).
%F a(n) = (n+1)*( (15*n^3 +55*n^2 +50*n +24)*L(n+2) + 2*(5*n^3 +15*n^2 +10*n +24)*L(n+1))/5!, with the Lucas numbers L(n)=A000032(n).
%F G.f.: ((1+2*x)/(1-x-x^2))^5.
%t Table[((n+1)/120)*((5*n^3+5*n^2-10*n+72)*LucasL[n+5] + 4*(5*n^2+10*n-24)*LucasL[n+ 4]), {n, 0, 40}] (* _G. C. Greubel_, Apr 08 2021 *)
%o (Magma)
%o R<x>:=PowerSeriesRing(Integers(), 40);
%o Coefficients(R!( ((1+2*x)/(1-x-x^2))^5 )); // _G. C. Greubel_, Apr 08 2021
%o (Sage)
%o def A060931_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( ((1+2*x)/(1-x-x^2))^5 ).list()
%o A060931_list(40) # _G. C. Greubel_, Apr 08 2021
%Y Cf. A000032, A000204, A004799, A060922, A060929, A060930.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Apr 20 2001
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