A101379 a(n) = n*(n+1)^2*(6*n^3-5*n^2+3*n+2)/24.

0, 1, 27, 256, 1325, 4815, 13916, 34272, 75006, 149925, 278905, 489456, 818467, 1314131, 2038050, 3067520, 4497996, 6445737, 9050631, 12479200, 16927785, 22625911, 29839832, 38876256, 50086250, 63869325, 80677701, 101020752, 125469631, 154662075, 189307390

Offset

0,3

References

T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.

Links

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

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

Formula

G.f.: x*(1 + 20*x + 88*x^2 + 65*x^3 + 6*x^4)/(1 - x)^7. - Ilya Gutkovskiy, Feb 24 2017

E.g.f.: exp(x)*x*(24 + 300*x + 712*x^2 + 459*x^3 + 97*x^4 + 6*x^5)/24. - Stefano Spezia, Sep 10 2022

Mathematica

Table[(n (1+n)^2 (2+n (3+n (-5+6 n))))/24, {n, 0, 40}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 27, 256, 1325, 4815, 13916}, 40] (* Harvey P. Dale, Jun 20 2021 *)

Prog

(Magma) [n*(n+1)^2*(6*n^3-5*n^2+3*n+2)/24: n in [0..40]]; // Vincenzo Librandi, Jun 15 2011
(PARI) a(n)=n*(n+1)^2*(6*n^3-5*n^2+3*n+2)/24 \\ Charles R Greathouse IV, Feb 24 2017

Crossrefs

Sequence in context: A042414 A099226 A016107 * A374894 A132652 A349507

Adjacent sequences: A101376 A101377 A101378 * A101380 A101381 A101382

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 15 2005

Status

approved