A071252 a(n) = n*(n - 1)*(n^2 + 1)/2.

0, 0, 5, 30, 102, 260, 555, 1050, 1820, 2952, 4545, 6710, 9570, 13260, 17927, 23730, 30840, 39440, 49725, 61902, 76190, 92820, 112035, 134090, 159252, 187800, 220025, 256230, 296730, 341852, 391935, 447330, 508400, 575520, 649077, 729470, 817110, 912420

Offset

0,3

References

T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = floor(n^5/(n+1))/2. - Gary Detlefs, Mar 31 2011

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) n>4, a(0)=0, a(1)=0, a(2)=5, a(3)=30, a(4)=102. - Yosu Yurramendi, Sep 03 2013

G.f.: x^2*(5+5*x+2*x^2)/(1-x)^5. - Joerg Arndt, Sep 04 2013

From Indranil Ghosh, Apr 05 2017: (Start)

a(n) = A002378(n) * A002522(n) / 2.

E.g.f.: exp(x)*x^2*(5 + 5*x + x^2)/2.

(End)

Mathematica

f[n_] := n (n - 1) (n^2 + 1)/2 (* Or *) f[n_] := Floor[n^5/(n + 1)]/2; Array[f, 38, 0] (* Robert G. Wilson v, Apr 01 2012 *)

Prog

(Magma) [n*(n-1)*(n^2+1)/2: n in [0..40]]; // Vincenzo Librandi, Jun 14 2011
(PARI) a(n)=n*(n-1)*(n^2+1)/2; \\ Joerg Arndt, Sep 04 2013
(Python) def a(n): return  n*(n - 1)*(n**2 + 1)/2 # Indranil Ghosh, Apr 05 2017
(SageMath)
def A071252(n): return binomial(n, 2)*(1+n^2)
[A071252(n) for n in range(41)] # G. C. Greubel, Aug 07 2024

Crossrefs

Cf. A002378, A002522, A071239, A071244, A071245, A071246.

Sequence in context: A128302 A258582 A288679 * A174002 A030506 A062990

Adjacent sequences: A071249 A071250 A071251 * A071253 A071254 A071255

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 12 2002

Status

approved