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

0,2

Links

Table of n, a(n) for n=0..29.

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

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A110675 A265805 A274270 * A055250 A038740 A225428

Adjacent sequences: A100787 A100788 A100789 * A100791 A100792 A100793

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 04 2005

Status

approved