cp's OEIS Frontend

A038166 G.f.: 1/((1-x)*(1-x^2))^6.

%I A038166 #13 Jul 08 2025 22:08:51
%S A038166 1,6,27,92,273,714,1715,3816,8007,15938,30381,55692,98735,169806,
%T A038166 284349,464672,742950,1164228,1791426,2710344,4037670,5928988,8591154,
%U A038166 12294672,17392258,24337404,33711510,46251016,62886162,84779748
%N A038166 G.f.: 1/((1-x)*(1-x^2))^6.
%H A038166 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (6, -9, -16, 60, -24, -116, 144, 66, -220, 66, 144, -116, -24, 60, -16, -9, 6, -1).
%F A038166 a(2*k) = binomial(k + 8, 8)*(2*k + 9)*(8*k^2 + 72*k + 55)/(11*5*9) = A059603(k); a(2*k + 1) = 2*binomial(k + 9, 9)*(8*k^2 + 80*k + 165)/(11*5) = 2*A059624(k), k >= 0; _Wolfdieter Lang_, Feb 02 2000
%F A038166 a(0)=1, a(1)=6, a(2)=27, a(3)=92, a(4)=273, a(5)=714, a(6)=1715, a(7)=3816, a(8)=8007, a(9)=15938, a(10)=30381, a(11)=55692, a(12)=98735, a(13)=169806, a(14)=284349, a(15)=464672, a(16)=742950, a(17)=1164228, a(n)=6*a(n-1)-9*a(n-2)-16*a(n-3)+60*a(n-4)-24*a(n-5)-116*a(n-6)+144*a(n-7)+ 66*a(n-8)- 220*a(n-9)+66*a(n-10)+144*a(n-11)-116*a(n-12)-24*a(n-13)+60*a(n-14)-16*a(n-15)- 9*a(n-16)+ 6*a(n-17)-a(n-18). - _Harvey P. Dale_, Jun 10 2013
%p A038166 A038166 := proc(n)
%p A038166     add( A038163(n-i)*A038163(i),i=0..n) ;
%p A038166 end proc:
%p A038166 seq(A038166(n),n=0..30) ;# _R. J. Mathar_, Feb 22 2021
%t A038166 CoefficientList[Series[1/((1-x)(1-x^2))^6,{x,0,40}],x] (* or *) LinearRecurrence[ {6,-9,-16,60,-24,-116,144,66,-220,66,144,-116,-24,60,-16,-9,6,-1},{1,6,27,92,273,714,1715,3816,8007,15938,30381,55692,98735,169806,284349,464672,742950,1164228},40] (* _Harvey P. Dale_, Jun 10 2013 *)
%Y A038166 Cf. A008619, A006918, A038163-A038165.
%K A038166 nonn,easy
%O A038166 0,2
%A A038166 _N. J. A. Sloane_