A101382 a(n) = n*(n+1)*(2*n^3 - n^2 + 2)^2/6.

0, 3, 196, 4418, 43320, 257645, 1108828, 3810996, 11105328, 28524615, 66322740, 142270678, 285547496, 541981713, 980925260, 1704069160, 2856536928, 4640618571, 7332534948, 11302649130, 17039568280, 25178606453, 36535105596, 52143138908, 73300147600

Offset

0,2

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 (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: x*(3 + 169*x + 2762*x^2 + 10362*x^3 + 10727*x^4 + 2749*x^5 + 108*x^6)/(1 - x)^9. - Ilya Gutkovskiy, Feb 24 2017

E.g.f.: x*(18 + 570*x + 3839*x^2 + 6703*x^3 + 4164*x^4 + 1061*x^5 + 112*x^6 + 4*x^7)*exp(x)/6. - G. C. Greubel, Mar 11 2021

Maple

A101382:= n-> n*(n+1)*(2*n^3-n^2+2)^2/6: seq(A101382(n), n=0..35); # G. C. Greubel, Mar 11 2021

Mathematica

Table[n*(n+1)*(2*n^3-n^2+2)^2/6, {n, 0, 35}] (* G. C. Greubel, Mar 11 2021 *)

Prog

(Magma) [n*(n+1)*(2*n^3-n^2+2)^2/6: n in [0..40]]; // Vincenzo Librandi, May 26 2011
(PARI) a(n)=n*(n+1)*(2*n^3-n^2+2)^2/6 \\ Charles R Greathouse IV, Feb 24 2017
(Sage) [n*(n+1)*(2*n^3-n^2+2)^2/6 for n in (0..35)] # G. C. Greubel, Mar 11 2021

Crossrefs

Cf. A101383.

Sequence in context: A332957 A203749 A093978 * A000724 A309749 A209120

Adjacent sequences: A101379 A101380 A101381 * A101383 A101384 A101385

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 15 2005

Status

approved