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) = 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)=4, a(3)=23, a(4)=76. - Yosu Yurramendi, Sep 03 2013
From Indranil Ghosh, Apr 05 2017: (Start)
G.f.: x^2*(4 + 3*x + x^2)/(1 - x)^5.
E.g.f.: exp(x)*x^2*(4+x)*(3+2*x)/6. (End)
MATHEMATICA
CoefficientList[Series[-(4x^2 + 3x^3 + x^4)/(x - 1)^5, {x, 0, 50}], x] (* or *) Table[n*(n - 1)*(2*n^2 + n + 2)/6, {n, 0, 50}] (* Indranil Ghosh, Apr 05 2017 *)
PROG
(Magma) [n*(n-1)*(2*n^2+n+2)/6: n in [0..40]]; // Vincenzo Librandi, Jun 14 2011
(PARI) a(n) = n*(n - 1)*(2*n^2 + n + 2)/6; \\ Indranil Ghosh, Apr 05 2017
(Python) def a(n): return n*(n - 1)*(2*n**2 + n + 2)/6 # Indranil Ghosh, Apr 05 2017
(SageMath)
def A071246(n): return binomial(n, 2)*(2+n+2*n^2)//3
[A071246(n) for n in range(41)] # G. C. Greubel, Aug 07 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 12 2002
STATUS
approved