A071237 a(n) = n*(n+1)*(n^2+1)/2.

0, 2, 15, 60, 170, 390, 777, 1400, 2340, 3690, 5555, 8052, 11310, 15470, 20685, 27120, 34952, 44370, 55575, 68780, 84210, 102102, 122705, 146280, 173100, 203450, 237627, 275940, 318710, 366270, 418965, 477152, 541200, 611490, 688415, 772380, 863802, 963110

Offset: 0

Author

N. J. A. Sloane, Jun 12 2002

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A027445, A037270.

Programs

Magma

[n*(n+1)*(n^2+1)/2: n in [0..40] ]; // Vincenzo Librandi, May 23 2011

Mathematica

Table[(n^4 + n^3 + n^2 + n)/2, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)
LinearRecurrence[{5,-10,10,-5,1},{0,2,15,60,170},40] (* Harvey P. Dale, Feb 08 2025 *)

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

Formula

From Arkadiusz Wesolowski, Apr 01 2012: (Start)

a(n) = A000217(n)*A002522(n).

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