A014205 (1/12)*(n+5)*(n+1)*n^2.

0, 1, 7, 24, 60, 125, 231, 392, 624, 945, 1375, 1936, 2652, 3549, 4655, 6000, 7616, 9537, 11799, 14440, 17500, 21021, 25047, 29624, 34800, 40625, 47151, 54432, 62524, 71485, 81375, 92256, 104192, 117249, 131495, 147000, 163836, 182077, 201799, 223080, 246000

Offset

0,3

Comments

Partial sums of A084990. - Arkadiusz Wesolowski, Jan 25 2014

Links

Vincenzo Librandi, 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(n) = 2*C(n+3,4) - C(n+1,2). - Zerinvary Lajos, May 02 2007

G.f.: x*(x^2-2*x-1)/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009

a(0)=0, a(1)=1, a(2)=7, a(3)=24, a(4)=60, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Aug 10 2014

Maple

seq(2*binomial(n+3, 4)-binomial(n+1, 2), n=0..32); # Zerinvary Lajos, May 02 2007

Mathematica

Table[((n+5)(n+1)n^2)/12, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 7, 24, 60}, 50] (* Harvey P. Dale, Aug 10 2014 *)
CoefficientList[Series[x (x^2 - 2 x - 1)/(x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 11 2014 *)

Prog

(Magma) [(1/12)*(n+5)*(n+1)*n^2: n in [0..50]]; // Vincenzo Librandi, Aug 11 2014
(PARI) a(n)=n^2*(n+1)*(n+5)/12 \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Cf. A084990.

Sequence in context: A024205 A008779 A062449 * A002969 A029585 A114291

Adjacent sequences: A014202 A014203 A014204 * A014206 A014207 A014208

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved