A168636 a(n) = n^7*(n^2 + 1)/2.

0, 1, 320, 10935, 139264, 1015625, 5178816, 20588575, 68157440, 196101729, 505000000, 1188717431, 2597806080, 5333623945, 10383230144, 19307109375, 34493956096, 59499107585, 99485755200, 161790784759, 256640000000, 398040567561, 604881787840, 902278743455

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A168635.

Programs

Magma

[n^7*(n^2+1)/2: n in [0..25]]; // Vincenzo Librandi, Jul 29 2016

Mathematica

Table[n^7 (n^2+1)/2,{n,0,20}] (* or *) LinearRecurrence[{10,-45,120,-210, 252, -210, 120, -45,10,-1}, {0,1, 320, 10935, 139264, 1015625, 5178816, 20588575, 68157440, 196101729}, 21] (* Harvey P. Dale, Mar 09 2016 *)

PARI

a(n)=n^7*(n^2+1)/2 \\ Charles R Greathouse IV, Jul 29 2016

SageMath

def A168636(n): return n^5*binomial(n^2+1,2)
print([A168636(n) for n in range(31)]) # G. C. Greubel, Mar 23 2025

Formula

From Harvey P. Dale, Mar 09 2016: (Start)

a(0)=0, a(1)=1, a(2)=320, a(3)=10935, a(4)=139264, a(5)=1015625, a(6)=5178816, a(7)=20588575, a(8)=68157440, a(9)=196101729, a(n)= 10*a(n-1)- 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10).

G.f.: x*(1 + 310*x + 7780*x^2 + 44194*x^3 + 76870*x^4 + 44194*x^5 + 7780*x^6 + 310*x^7 + x^8)/(1 - x)^10. (End)

E.g.f.: (1/2)*x*(2 + 318*x + 3326*x^2 + 8120*x^3 + 7091*x^4 + 2667*x^5 + 463*x^6 + 36*x^7 + x^8)*exp(x). - G. C. Greubel, Jul 28 2016