login
Expansion of 1/((1+x)*(1-x)^10).
3

%I #21 Sep 08 2022 08:44:29

%S 1,9,46,174,541,1461,3544,7896,16414,32206,60172,107788,186142,311278,

%T 505912,801592,1241383,1883167,2803658,4103242,5911763,8395387,

%U 11764688,16284112,22282988,30168268,40439192

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

%H Vincenzo Librandi, <a href="/A001781/b001781.txt">Table of n, a(n) for n = 0..10000</a>

%H <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 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 a(n)+a(n+1) = A000582(n+10). - _R. J. Mathar_, Jan 06 2021

%p 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 seq(A001781(n),n=0..50) ; # _R. J. Mathar_, Mar 22 2011

%o (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 (PARI) Vec(1/(1+x)/(1-x)^10+O(x^99)) \\ _Charles R Greathouse IV_, Apr 18 2012

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_