login
First differences of A047780.
1

%I #11 Oct 21 2022 21:40:54

%S 1,9,47,183,560,1426,3164,6322,11643,20095,32901,51569,77922,114128,

%T 162730,226676,309349,414597,546763,710715,911876,1156254,1450472,

%U 1801798,2218175,2708251,3281409,3947797,4718358,5604860

%N First differences of A047780.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).

%F (1/24)(n+1)(6n^4+9n^3+23n^2+46n+24). - _Ralf Stephan_, May 16 2007

%F a(0)=1, a(1)=9, a(2)=47, a(3)=183, a(4)=560, a(5)=1426, a(n)= 6*a(n-1)- 15*a(n-2)+ 20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - _Harvey P. Dale_, Dec 18 2013

%t Differences[CoefficientList[Series[x (1+3x+8x^2+16x^3+2x^4)/(1-x)^7,{x,0,50}],x]] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,9,47,183,560,1426},50] (* _Harvey P. Dale_, Dec 18 2013 *)

%o (PARI) a(n)=(n+1)(6*n^4+9*n^3+23*n^2+46*n+24)/24 \\ _Charles R Greathouse IV_, Oct 21 2022

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jan 04 2005