A132764 - OEIS
0, 23, 48, 75, 104, 135, 168, 203, 240, 279, 320, 363, 408, 455, 504, 555, 608, 663, 720, 779, 840, 903, 968, 1035, 1104, 1175, 1248, 1323, 1400, 1479, 1560, 1643, 1728, 1815, 1904, 1995, 2088, 2183, 2280, 2379, 2480, 2583, 2688, 2795, 2904, 3015, 3128, 3243, 3360
FORMULA
a(n) = n*(n + 22).
a(n) = 2*n + a(n-1) + 21 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
a(0)=0, a(1)=23, a(2)=48, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 02 2012
Sum_{n>=1} 1/a(n) = H(22)/22 = A001008(22)/A102928(22) = 19093197/113809696, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 156188887/5121436320. (End)
G.f.: x*(23 - 21*x)/(1-x)^3.
E.g.f.: x*(23 + x)*exp(x). (End)
EXAMPLE
a(1)=2*1+0+21=23; a(2)=2*2+23+21=48; a(3)=2*3+48+21=75. - Vincenzo Librandi, Aug 03 2010
MATHEMATICA
Table[n(n+22), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 23, 48}, 50] (* Harvey P. Dale, May 02 2012 *)
PROG
(Sage) [n*(n+22) for n in (0..50)] # G. C. Greubel, Mar 14 2022