A196506 a(n) = 1*3*5 + 3*5*7 + 5*7*9 + ... (n terms).

0, 15, 120, 435, 1128, 2415, 4560, 7875, 12720, 19503, 28680, 40755, 56280, 75855, 100128, 129795, 165600, 208335, 258840, 318003, 386760, 466095, 557040, 660675, 778128, 910575, 1059240, 1225395, 1410360, 1615503, 1842240, 2092035

Offset: 0

Author

R. J. Mathar, Oct 03 2011

Keywords

• nonn
• easy

Comments

All terms are multiples of 3.

References

• Jolley, Summation of Series, Dover (1961), eq (43) page 8.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A061550 (first differences).

Programs

Magma

[((4*n^2-1)*(2*n+3)*(2*n+5)+15)/ 8 : n in [0..30]]; // Vincenzo Librandi, Oct 05 2011

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{0,15,120,435,1128},40] (* or *) Accumulate[ Join[{0},Times@@@Partition[Range[1,111,2],3,1]]] (* or *) Table[2n^4-5n^2+3,{n,40}](* Harvey P. Dale, Mar 14 2015 *)

Formula

a(n) = ((4n^2 - 1)*(2n + 3)*(2n + 5) + 15)/ 8 = Sum_{i=1..n} (2i - 1)*(2i + 1)*(2i + 3).

G.f. -3*x*(5 + 15*x - 5*x^2 + x^3) / (x-1)^5 .

a(n) = 2 n^4 + 8 n^3 + 7 n^2 - 2 n. - Harvey P. Dale, Mar 14 2015, corrected by Eric Rowland, Aug 15 2017