|
%I #19 Oct 20 2022 03:34:45
%S 4,20,104,552,2972,16172,88720,489872,2719028,15157188,84799992,
%T 475894200,2677788492,15102309468,85347160608,483183316512,
%U 2739851422820,15558315261812,88462135512712,503569008273992,2869602773253884,16368396446913420,93449566652932784
%N First differences of A002002.
%H G. C. Greubel, <a href="/A035028/b035028.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = A049600(n, n-3).
%F D-finite with recurrence: (n+2)*a(n) - (7*n+8)*a(n-1) + (7*n-8)*a(n-2) - (n-2)*a(n-3) = 0. - _R. J. Mathar_, Jan 28 2020
%F a(n) = ((n+1)*(n+3)*A001850(n+3) - (6*n^2 +22*n +17)*A001850(n+2) + (n+2)*(5*n+8)*A001850(n+1))/(2*(n+1)*(n+2)), A001850(n) = LegrndreP(n, 3). - _G. C. Greubel_, Oct 19 2022
%t Differences[CoefficientList[Series[((1-x)/Sqrt[1-6x+x^2]-1)/2, {x,0,30}], x]] (* _Harvey P. Dale_, Jun 04 2011 *)
%t With[{P=LegendreP}, Table[(n*(n+2)*P[n+2,3] -(6*n^2+10*n+1)*P[n+1,3] +(n+1)*(5*n+ 3)*P[n,3])/(2*n*(n+1)), {n,30}]] (* _G. C. Greubel_, Oct 19 2022 *)
%o (Magma) I:=[4,20,104]; [n le 3 select I[n] else ( (7*n+1)*Self(n-1) - (7*n-15)*Self(n-2) + (n-3)*Self(n-3) )/(n+1): n in [1..30]]; // _G. C. Greubel_, Oct 19 2022
%o (SageMath)
%o def A001850(n): return gen_legendre_P(n,0,3)
%o def A035028(n): return ((n+1)*(n+3)*A001850(n+3) - (6*n^2 +22*n +17)*A001850(n+2) + (n+2)*(5*n+8)*A001850(n+1))/(2*(n+1)*(n+2))
%o [A035028(n) for n in range(40)] # _G. C. Greubel_, Oct 19 2022
%Y Cf. A001850, A002002, A035029, A049600.
%K nonn
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Harvey P. Dale_, Jun 04 2011
|
