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
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).
Crossrefs
Cf. A271535.
Programs
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Magma
[n^3*(2*n^2+1)/3: n in [0..40]];
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Mathematica
Table[n^3 (2 n^2 + 1)/3, {n, 0, 40}] -
PARI
vector(100, n, n--; n^3*(2*n^2+1)/3) \\ Altug Alkan, Apr 22 2016
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).
Comments