cp's OEIS Frontend

A001779 Expansion of 1/((1+x)(1-x)^8).

%I A001779 #38 Jan 18 2024 09:49:58
%S A001779 1,7,29,91,239,553,1163,2269,4166,7274,12174,19650,30738,46782,69498,
%T A001779 101046,144111,201993,278707,379093,508937,675103,885677,1150123,
%U A001779 1479452,1886404,2385644,2993972
%N A001779 Expansion of 1/((1+x)(1-x)^8).
%C A001779 a(n) is the number of positive terms in the expansion of (a_1 + a_2 + a_3 + a_4 + a_5 + a_6 + a_7 - z)^n. Also the convolution of A001769 and A000012; A001753 and A001477; A001752 and A000217; A002623 and A000292; A002620 and A000332; A004526 and A000389. - Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Feb 13 2007
%H A001779 Vincenzo Librandi, <a href="/A001779/b001779.txt">Table of n, a(n) for n = 0..10000</a>
%H A001779 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (7,-20,28,-14,-14,28,-20,7,-1).
%F A001779 a(n) = (-1)^{7-n}*Sum_{i=0..n} ((-1)^(7-i)*binomial(7+i,i)). - _Sergio Falcon_, Feb 13 2007
%F A001779 a(n)+a(n+1) = A000580(n+8). - _R. J. Mathar_, Jan 06 2021
%p A001779 A001779 := proc(n) 1/80640*(2*n+9) *(4*n^6 +108*n^5 +1138*n^4 +5904*n^3 +15628*n^2 +19638*n +8925)+(-1)^n/256 ; end proc:
%p A001779 seq(A001779(n),n=0..50) ; # _R. J. Mathar_, Mar 22 2011
%t A001779 CoefficientList[Series[1/((1 + x) (1 - x)^8), {x, 0, 50}], x] (* _G. C. Greubel_, Nov 24 2017 *)
%t A001779 LinearRecurrence[{7,-20,28,-14,-14,28,-20,7,-1},{1,7,29,91,239,553,1163,2269,4166},30] (* _Harvey P. Dale_, Jan 21 2023 *)
%o A001779 (Magma) [1/80640*(2*n+9) *(4*n^6 +108*n^5 +1138*n^4 +5904*n^3 +15628*n^2 +19638*n +8925)+(-1)^n/256 : n in [0..30]]; // _Vincenzo Librandi_, Oct 08 2011
%o A001779 (PARI) a(n)=(2*n+9)*(4*n^6+108*n^5+1138*n^4+5904*n^3+15628*n^2+19638*n + 8925)/80640 +(-1)^n/256 \\ _Charles R Greathouse IV_, Apr 17 2012
%Y A001779 Cf. A001769 (first differences), A169795 (binomial transf.)
%K A001779 nonn,easy
%O A001779 0,2
%A A001779 _N. J. A. Sloane_