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A001786 Expansion of 1/((1+x)*(1-x)^11).

%I A001786 #35 Apr 21 2025 10:46:26
%S A001786 1,10,56,230,771,2232,5776,13672,30086,62292,122464,230252,416394,
%T A001786 727672,1233584,2035176,3276559,5159726,7963384,12066626,17978389,
%U A001786 26373776,38138464,54422576,76705564,106873832,147313024,201017112,271716644,364028752,483631776,637467632,833975341
%N A001786 Expansion of 1/((1+x)*(1-x)^11).
%H A001786 Vincenzo Librandi, <a href="/A001786/b001786.txt">Table of n, a(n) for n = 0..1000</a>
%H A001786 Jia Huang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Huang/huang8.html">Partially Palindromic Compositions</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 17.
%H A001786 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (10,-44,110,-165,132,0,-132,165,-110,44,-10,1).
%F A001786 Boas-Buck recurrence: a(n) = (1/n)*Sum_{p=0..n-1} (11 + (-1)^(n-p))*a(p), n >= 1, a(0) = 1. See the Boas-Buck comment in A046521 (here for the unsigned column k = 5 with offset 0). - _Wolfdieter Lang_, Aug 10 2017
%t A001786 CoefficientList[Series[1/((1+x)(1-x)^11),{x,0,50}],x] (* _Vincenzo Librandi_, Feb 24 2012 *)
%t A001786 LinearRecurrence[{10,-44,110,-165,132,0,-132,165,-110,44,-10,1},{1,10,56,230,771,2232, 5776,13672,30086,62292,122464,230252},30] (* _Harvey P. Dale_, Oct 22 2015 *)
%o A001786 (Magma)
%o A001786 R<x>:=PowerSeriesRing(Integers(), 50);
%o A001786 Coefficients(R!( 1/((1+x)*(1-x)^11) )); // _G. C. Greubel_, Apr 20 2025
%o A001786 (SageMath)
%o A001786 def A001786_list(prec):
%o A001786     P.<x> = PowerSeriesRing(ZZ, prec)
%o A001786     return P( 1/((1+x)*(1-x)^11) ).list()
%o A001786 print(A001786_list(50)) # _G. C. Greubel_, Apr 20 2025
%Y A001786 Cf. A001780, A158454 (signed column k=5).
%Y A001786 Eleventh column of A112465.
%K A001786 nonn,easy
%O A001786 0,2
%A A001786 _N. J. A. Sloane_