%I #32 Jun 28 2023 22:10:37

%S 8,36,224,756,1232,2808,5544,7488,12852,20672,25704,38456,55440,65780,

%T 90720,122148,140616,183744,236096,266112,334628,415584,461168,563472,

%U 681912,747684,893376,1059380,1150560,1350440,1575288,1697696,1963764,2259936,2419992

%N Positive integers of the form n(n+1)(n+2)(n+3)(n+4)/(n+(n+1)+(n+2)+(n+3)+(n+4)) that are a multiple of n.

%H Colin Barker, <a href="/A032794/b032794.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,4,-4,0,-6,6,0,4,-4,0,-1,1).

%F From _Colin Barker_, May 30 2019: (Start)

%F G.f.: 4*x*(2 + 7*x + 47*x^2 + 125*x^3 + 91*x^4 + 206*x^5 + 164*x^6 + 52*x^7 + 47*x^8 + 9*x^9) / ((1 - x)^5*(1 + x + x^2)^4).

%F a(n) = a(n-1) + 4*a(n-3) - 4*a(n-4) - 6*a(n-6) + 6*a(n-7) + 4*a(n-9) - 4*a(n-10) - a(n-12) + a(n-13) for n>13.

%F (End)

%o (PARI) Vec(4*x*(2 + 7*x + 47*x^2 + 125*x^3 + 91*x^4 + 206*x^5 + 164*x^6 + 52*x^7 + 47*x^8 + 9*x^9) / ((1 - x)^5*(1 + x + x^2)^4) + O(x^40)) \\ _Colin Barker_, May 30 2019

%Y Cf. A032793, A032795.

%K nonn,easy

%O 1,1

%A _Patrick De Geest_, May 15 1998

%E Edited and offset changed by _Alois P. Heinz_, May 29 2019