A111991 - OEIS

%I #10 Jul 31 2015 18:05:23

%S 1,18,216,2136,18864,154656,1203072,9000576,65339136,463112704,

%T 3219204096,22019254272,148577427456,990973034496,6543595044864,

%U 42832379117568,278217855664128,1794871415144448,11508930723708928

%N Second convolution of A111989.

%H Vincenzo Librandi, <a href="/A111991/b111991.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (18, -108, 192, 288, -864, -192, 1152, 0, -512).

%F G.f.: 1/(1-6*x+8*x^3)^3.

%F a(n) = (2*(n+1)*b(n+1)-(n+6)*b(n)-4*(n+5)*b(n-1))/(2*9), with b(n):=A111990(n).

%F a(n) = ((35*n^2+75*n+54)*c(n)-4*(n+2)*(2*n-1)*c(n-1)-48*(n+1)^2*c(n-2))/54, with c(n):= A111989(n), especially, c(-2) = 0 = c(-1).

%F a(0)=1, a(1)=18, a(2)=216, a(3)=2136, a(4)=18864, a(5)=154656, a(6)=1203072, a(7)=9000576, a(8)=65339136, a(n)=18*a(n-1)- 108*a(n-2)+ 192*a(n-3)+ 288*a(n-4) -864*a(n-5)-192*a(n-6)+1152*a(n-7)-512*a(n-9). - _Harvey P. Dale_, Oct 10 2013

%t CoefficientList[Series[1/(1-6x+8x^3)^3,{x,0,30}],x] (* or *) LinearRecurrence[{18,-108,192,288,-864,-192,1152,0,-512},{1,18,216,2136,18864,154656,1203072,9000576,65339136},30] (* _Harvey P. Dale_, Oct 10 2013 *)

%Y Cf. A111990 (first convolution of A111989), A112003 (third convolution).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Sep 12 2005