A272125 a(n) = n^3*(2*n^2+1)/3.

0, 1, 24, 171, 704, 2125, 5256, 11319, 22016, 39609, 67000, 107811, 166464, 248261, 359464, 507375, 700416, 948209, 1261656, 1653019, 2136000, 2725821, 3439304, 4294951, 5313024, 6515625, 7926776, 9572499, 11480896, 13682229, 16209000, 19096031, 22380544, 26102241

Offset

0,3

Comments

Partial sums are in A271535.

After 1, is A195279 the second bisection?

Links

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

R. D. Carmichael and T. L. DeLand, Find the sum of the series 1^2 + 5^2 + 14^2 + 30^2 + ... + [n*(n+1)*(2*n+1)/6]^2, American Mathematical Monthly, Vol. 15, No. 6/7, Jun-Jul, 1908, pp. 132-133.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

O.g.f.: x*(1+18*x+42*x^2+18*x^3+x^4)/(1-x)^6.

E.g.f.: x*(3+33*x+51*x^2+20*x^3+2*x^4)*exp(x)/3.

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).

Mathematica

Table[n^3 (2 n^2 + 1)/3, {n, 0, 40}]

Prog

(Magma) [n^3*(2*n^2+1)/3: n in [0..40]];
(PARI) vector(100, n, n--; n^3*(2*n^2+1)/3) \\ Altug Alkan, Apr 22 2016

Crossrefs

Cf. A271535.

Sequence in context: A288486 A223291 A221069 * A166756 A268623 A209716

Adjacent sequences: A272122 A272123 A272124 * A272126 A272127 A272128

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 22 2016

Status

approved