A168661 a(n) = n^7*(n^4 + 1)/2.

0, 1, 1088, 89667, 2105344, 24453125, 181538496, 989075143, 4296015872, 15692921289, 50005000000, 142665578891, 371522101248, 896111571277, 2024835291584, 4324963359375, 8796227239936, 17136153323153, 32134511149632, 58245576384979, 102400640000000, 175139650815381, 292160397884608

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Crossrefs

Cf. A168635.

Programs

Magma

[n^7*(n^4+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

Mathematica

Table[n^7*(n^4 + 1)/2, {n,0,25}] (* G. C. Greubel, Jul 28 2016 *)

PARI

a(n)=n^7*(n^4+1)/2 \\ Charles R Greathouse IV, Jul 29 2016

SageMath

def A168661(n): return n^3*binomial(n^4+1,2)
print([A168661(n) for n in range(31)]) # G. C. Greubel, Mar 24 2025

Formula

From G. C. Greubel, Jul 28 2016: (Start)

G.f.: x*(1 + 1076*x + 76677*x^2 + 1100928*x^3 + 4868154*x^4 + 7864728*x^5 + 4868154*x^6 + 1100928*x^7 + 76677*x^8 + 1076*x^9 + x^10)/(1 - x)^12.

E.g.f.: (1/2)*x*(2 + 1086*x + 28802*x^2 + 146100*x^3 + 246870*x^4 + 179508*x^5 + 63988*x^6 + 11880*x^7 + 1155*x^8 + 55*x^9 + x^10)*exp(x). (End)