A057675 1 - (5/6)*n + (5/2)*n^2 + (10/3)*n^3 + n^4.

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

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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

Adjacent sequences: A057672 A057673 A057674 * A057676 A057677 A057678

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 19 2000

Status

approved