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A001781 Expansion of 1/((1+x)*(1-x)^10).

%I A001781 #27 Apr 21 2025 10:46:22
%S A001781 1,9,46,174,541,1461,3544,7896,16414,32206,60172,107788,186142,311278,
%T A001781 505912,801592,1241383,1883167,2803658,4103242,5911763,8395387,
%U A001781 11764688,16284112,22282988,30168268,40439192,53704088,70699532,92312108,119603024,153835856,196507709,249384101
%N A001781 Expansion of 1/((1+x)*(1-x)^10).
%H A001781 Vincenzo Librandi, <a href="/A001781/b001781.txt">Table of n, a(n) for n = 0..10000</a>
%H A001781 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (9,-35,75,-90,42,42,-90,75,-35,9,-1).
%F A001781 a(n) = +9*a(n-1) -35*a(n-2) +75*a(n-3) -90*a(n-4) +42*a(n-5) +42*a(n-6) -90*a(n-7) +75*a(n-8) -35*a(n-9) +9*a(n-10) -a(n-11). - _R. J. Mathar_, Mar 22 2011
%F A001781 a(n) + a(n+1) = A000582(n+10). - _R. J. Mathar_, Jan 06 2021
%p A001781 A001781 := proc(n) 1/2903040*(2*n+11) *(2*n^8 +88*n^7 +1616*n^6 +16060*n^5 +93656*n^4 +324808*n^3 +646236*n^2 +663894*n +263655)+(-1)^n/1024 ; end proc:
%p A001781 seq(A001781(n),n=0..50) ; # _R. J. Mathar_, Mar 22 2011
%o A001781 (Magma) [1/2903040*(2*n+11) *(2*n^8 +88*n^7 +1616*n^6 +16060*n^5 +93656*n^4 +324808*n^3 +646236*n^2 +663894*n +263655)+(-1)^n/1024  : n in [0..30]]; // _Vincenzo Librandi_, Oct 08 2011
%o A001781 (Magma)
%o A001781 R<x>:=PowerSeriesRing(Integers(), 50);
%o A001781 Coefficients(R!( 1/((1+x)*(1-x)^10) )); // _G. C. Greubel_, Apr 20 2025
%o A001781 (PARI) Vec(1/(1+x)/(1-x)^10+O(x^99)) \\ _Charles R Greathouse IV_, Apr 18 2012
%o A001781 (SageMath)
%o A001781 def A001781_list(prec):
%o A001781     P.<x> = PowerSeriesRing(ZZ, prec)
%o A001781     return P( 1/((1+x)*(1-x)^10) ).list()
%o A001781 print(A001781_list(50)) # _G. C. Greubel_, Apr 20 2025
%Y A001781 Cf. A000582.
%Y A001781 Tenth column of A112465.
%K A001781 nonn,easy
%O A001781 0,2
%A A001781 _N. J. A. Sloane_