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A057675
1 - (5/6)*n + (5/2)*n^2 + (10/3)*n^3 + n^4.
1
1, 7, 52, 192, 507, 1101, 2102, 3662, 5957, 9187, 13576, 19372, 26847, 36297, 48042, 62426, 79817, 100607, 125212, 154072, 187651, 226437, 270942, 321702, 379277, 444251, 517232, 598852, 689767, 790657, 902226, 1025202, 1160337
OFFSET
0,2
FORMULA
a(0)=1, a(1)=7, a(2)=52, a(3)=192, a(4)=507, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Apr 28 2016
G.f.: (1+2*x+27x^2-8*x^3+2*x^4)/(1-x)^5. - Vincenzo Librandi, Apr 30 2016
MATHEMATICA
Table[1-(5n)/6+(5n^2)/2+(10n^3)/3+n^4, {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 7, 52, 192, 507}, 40] (* Harvey P. Dale, Apr 28 2016 *)
CoefficientList[Series[(1 + 2 x + 27 x^2 - 8 x^3 + 2 x^4)/(1 - x)^5, {x, 0, 33}], x] (* Vincenzo Librandi, Apr 30 2016 *)
PROG
(Magma) [1-(5/6)*n+(5/2)*n^2+(10/3)*n^3+n^4: n in [0..50]]; // Vincenzo Librandi, Apr 30 2016
(PARI) a(n)=n^4 + 10/3*n^3 + 5/2*n^2 - 5/6*n + 1 \\ Charles R Greathouse IV, Apr 30 2016
CROSSREFS
Sequence in context: A156751 A352242 A138849 * A206809 A027542 A254946
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 19 2000
STATUS
approved