A163815 a(n) = n*(2*n^2 + 5*n + 3).

0, 10, 42, 108, 220, 390, 630, 952, 1368, 1890, 2530, 3300, 4212, 5278, 6510, 7920, 9520, 11322, 13338, 15580, 18060, 20790, 23782, 27048, 30600, 34450, 38610, 43092, 47908, 53070, 58590, 64480, 70752, 77418, 84490, 91980, 99900, 108262, 117078, 126360, 136120

Offset: 0

Author

Vincenzo Librandi, Aug 04 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A155151, A160378.

Programs

Mathematica

CoefficientList[Series[2*x*(5+x)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 10, 42, 108}, 50](* Vincenzo Librandi, Mar 06 2012 *)

PARI

x='x+O('x^50); concat([0], Vec(2*x*(5+x)/(x-1)^4)) \\ G. C. Greubel, Aug 04 2017

Formula

Row sums from A155151: a(n) = Sum_{m=1..n} 2*(2*m*n + m + n + 1).

a(n) = 2*A160378(n+1).

G.f.: 2*x*(5+x)/(x-1)^4.

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

E.g.f.: (2*x^3 + 11*x^2 + 10*x)*exp(x). - G. C. Greubel, Aug 04 2017

Extensions

Edited and a(4) corrected by R. J. Mathar, Aug 05 2009