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A100790
First differences of A047780.
1
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
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 04 2005
STATUS
approved