A101381 a(n) = n^2*(n+1)^2*(4*n^2 - 5*n + 4)/12.

0, 1, 30, 300, 1600, 5925, 17346, 43120, 95040, 191025, 356950, 628716, 1054560, 1697605, 2638650, 3979200, 5844736, 8388225, 11793870, 16281100, 22108800, 29579781, 39045490, 50910960, 65640000, 83760625, 105870726, 132643980, 164836000, 203290725, 248947050

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 + 23*x + 111*x^2 + 95*x^3 + 10*x^4) / (1-x)^7. - R. J. Mathar, Jun 15 2011

E.g.f.: x*(12 + 168*x + 426*x^2 + 288*x^3 + 63*x^4 + 4*x^5)*exp(x)/12. - G. C. Greubel, Mar 11 2021

Maple

A101381:= n-> n^2*(n+1)^2*(4*n^2-5*n+4)/12: seq(A101381(n), n=0..35); # G. C. Greubel, Mar 11 2021

Mathematica

Table[n^2 (n+1)^2 (4n^2-5n+4)/12, {n, 0, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 30, 300, 1600, 5925, 17346}, 40] (* Harvey P. Dale, Feb 03 2021 *)

Prog

(Magma) [n^2*(n+1)^2*(4*n^2-5*n+4)/12: n in [0..40]]; // Vincenzo Librandi, Jun 15 2011
(PARI) vector(35, n, my(m=n-1); m^2*(m+1)^2*(4*m^2-5*m+4)/12) \\ G. C. Greubel, Mar 11 2021
(Sage) [n^2*(n+1)^2*(4*n^2-5*n+4)/12 for n in (0..35)] # G. C. Greubel, Mar 11 2021

Crossrefs

Sequence in context: A229427 A113754 A129029 * A061605 A125393 A126551

Adjacent sequences: A101378 A101379 A101380 * A101382 A101383 A101384

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 15 2005

Status

approved