OFFSET
0,2
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
FORMULA
From Arkadiusz Wesolowski, Apr 01 2012: (Start)
a(0) = 0, a(1) = 2; for n >= 2, a(n) = ceiling(n^5/(2*n-2)) - 1.
G.f.: x*(2 + 5*x*(1 + x))/(1 - x)^5. (End)
a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5) for n>4, a(0)=0, a(1)=2, a(2)=15, a(3)=60, a(4)=170. - Yosu Yurramendi, Sep 03 2013
E.g.f.: (1/2)*x*(4 + 11*x + 7*x^2 + x^3)*exp(x). - G. C. Greubel, Aug 05 2024
MATHEMATICA
Table[(n^4 + n^3 + n^2 + n)/2, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)
PROG
(Magma) [n*(n+1)*(n^2+1)/2: n in [0..40] ]; // Vincenzo Librandi, May 23 2011
(SageMath)
def A071237(n): return (n^2+1)*binomial(n+1, 2)
[A071237(n) for n in range(51)] # G. C. Greubel, Aug 05 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 12 2002
STATUS
approved