A100790 First differences of A047780.

1, 9, 47, 183, 560, 1426, 3164, 6322, 11643, 20095, 32901, 51569, 77922, 114128, 162730, 226676, 309349, 414597, 546763, 710715, 911876, 1156254, 1450472, 1801798, 2218175, 2708251, 3281409, 3947797, 4718358, 5604860

Offset: 0

Author

N. J. A. Sloane, Jan 04 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Programs

Mathematica

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 *)

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

Formula

(1/24)(n+1)(6n^4+9n^3+23n^2+46n+24). - Ralf Stephan, May 16 2007

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