A163673 a(n) = n*(2*n^2 + 5*n + 15)/2.

0, 11, 33, 72, 134, 225, 351, 518, 732, 999, 1325, 1716, 2178, 2717, 3339, 4050, 4856, 5763, 6777, 7904, 9150, 10521, 12023, 13662, 15444, 17375, 19461, 21708, 24122, 26709, 29475, 32426, 35568, 38907, 42449, 46200, 50166

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

Row sums from A163672: a(n) = Sum_{m=1..n} (2*m*n + m + n + 7) = A163661(n) - n.

G.f.: x*(11 - 11*x + 6*x^2)/(x-1)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

E.g.f.: (1/2)*x*(22 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 02 2017

Mathematica

CoefficientList[Series[x*(11-11*x+6*x^2)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 11, 33, 72}, 50] (* Vincenzo Librandi, Mar 06 2012 *)
Table[n (2n^2+5n+15)/2, {n, 0, 60}] (* Harvey P. Dale, Apr 01 2023 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(x*(11-11*x+6*x^2)/(x-1)^4)) \\ G. C. Greubel, Aug 02 2017

Crossrefs

Cf. A163672, A163661.

Sequence in context: A152740 A080859 A063036 * A212132 A027025 A366135

Adjacent sequences: A163670 A163671 A163672 * A163674 A163675 A163676

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 03 2009

Extensions

Edited by R. J. Mathar, Aug 05 2009

Status

approved