A130862 a(n) = (n-1)*(n+2)*(2*n+11)/2.

0, 30, 85, 171, 294, 460, 675, 945, 1276, 1674, 2145, 2695, 3330, 4056, 4879, 5805, 6840, 7990, 9261, 10659, 12190, 13860, 15675, 17641, 19764, 22050, 24505, 27135, 29946, 32944, 36135, 39525, 43120, 46926, 50949, 55195, 59670, 64380, 69331, 74529, 79980, 85690, 91665, 97911, 104434, 111240, 118335, 125725, 133416, 141414

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = (5/2)*(n+2)*(n+3)*(Sum_{j=1..n} Sum_{m=1..j} Sum_{k=1..m} (k^2-1))/(Sum_{j=1..n} Sum_{m=1..j} Sum_{k=1..m} k) = (5/2)*(n+2)*(n+3)*A130857(n)/A000332(n+3).

G.f.: x^2*(30-35*x+11*x^2)/(-1+x)^4. - R. J. Mathar, Nov 14 2007

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=0, a(2)=30, a(3)=85, a(4)=171. - Harvey P. Dale, May 01 2011

From Amiram Eldar, Jul 04 2026: (Start)

Sum_{n>=2} 1/a(n) = 3721/1366365 + 8*log(2)/91.

Sum_{n>=2} (-1)^n/a(n) = 40*log(2)/273 - 2*Pi/91 - 3277/455455. (End)

Mathematica

Rest[CoefficientList[Series[x^2(30-35x+11x^2)/(-1+x)^4, {x, 0, 30}], x]] (* Harvey P. Dale, May 01 2011 *)
(* Alternative: *)
LinearRecurrence[{4, -6, 4, -1}, {0, 30, 85, 171}, 30] (* Harvey P. Dale, May 01 2011 *)

Prog

(Magma) [(n-1)*(n+2)*(2*n+11)/2: n in [1..50]]; // Vincenzo Librandi, May 02 2011
(PARI) a(n)=(2*n^3 + 13*n^2 + 7*n - 22)/2 \\ Charles R Greathouse IV, May 02 2011

Crossrefs

Cf. A000332, A055998, A130857.

Sequence in context: A326309 A326838 A098996 * A070756 A058903 A254474

Adjacent sequences: A130859 A130860 A130861 * A130863 A130864 A130865

Keyword

nonn,easy,changed

Author

Roger L. Bagula, Jul 22 2007

Extensions

Edited by N. J. A. Sloane, May 01 2011

Status

approved