A165187 a(n) = n^3*(n+1)^2*(n+2)/12.

1, 24, 180, 800, 2625, 7056, 16464, 34560, 66825, 121000, 207636, 340704, 538265, 823200, 1224000, 1775616, 2520369, 3508920, 4801300, 6468000, 8591121, 11265584, 14600400, 18720000, 23765625, 29896776, 37292724, 46154080, 56704425, 69192000, 83891456, 101105664

Offset

1,2

Comments

a(n) is row 30 of Table A128629 and can be generated by multiplying rows

two, three and five (or any other combination of rows with a row number product of 30).

Links

Table of n, a(n) for n=1..32.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = A000027(n)*A000217(n)*A000292(n) = A128629(30,n).

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).

G.f.: -x*(1+17*x+33*x^2+9*x^3)/(x-1)^7.

From Amiram Eldar, Feb 13 2023: (Start)

Sum_{n>=1} 1/a(n) = 153/4 - 9*Pi^2/2 + 6*zeta(3).

Sum_{n>=1} (-1)^(n+1)/a(n) = 48*log(2) - 141/4 - Pi^2/4 + 9*zeta(3)/2. (End)

Example

1,2,3,4,5, ... (A000027) times 1,3,6,10,15, ... (A000217) times 1,4,10,20,35, ... (A000292) yields 1,24,180,800, ...

Mathematica

a[n_] := n^3*(n+1)^2*(n+2)/12; Array[a, 35] (* Amiram Eldar, Feb 13 2023 *)

Crossrefs

Cf. A000027, A000217, A000292, A128629.

Sequence in context: A209986 A372521 A297522 * A052761 A371158 A371198

Adjacent sequences: A165184 A165185 A165186 * A165188 A165189 A165190

Keyword

nonn,easy

Author

Alford Arnold, Sep 06 2009

Extensions

Edited and extended by R. J. Mathar, Sep 09 2009

Status

approved