A168029 a(n) = n*(n^6 + 1)/2.

0, 1, 65, 1095, 8194, 39065, 139971, 411775, 1048580, 2391489, 5000005, 9743591, 17915910, 31374265, 52706759, 85429695, 134217736, 205169345, 306110025, 446935879, 640000010, 900544281, 1247178955, 1702412735, 2293235724, 3051757825, 4015905101

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy
• changed

Links

• Kelvin Voskuijl, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Sequences of the form n*(n^m + 1)/2: A001477 (m=0), A000217 (m=1), A006003 (m=2), A027441 (m=3), A021003 (m=4), A167963 (m=5), this sequence (m=6), A168067 (m=7), A168116 (m=8), A168118 (m=9), A168119 (m=10).

Programs

Magma

[n*(n^6+1)/2: n in [0..40]]; // Vincenzo Librandi, Dec 10 2014

Mathematica

CoefficientList[Series[x(1 +57x +603x^2 +1198x^3 +603x^4 +57x^5 +x^6)/ (1-x)^8, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 10 2014 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1}, {0,1,65,1095,8194,39065, 139971,411775}, 41] (* Harvey P. Dale, Jan 24 2019 *)

SageMath

[n*(n^6+1)/2 for n in range(41)] # G. C. Greubel, Jan 12 2023

Formula

G.f.: x*(1+57*x+603*x^2+1198*x^3+603*x^4+57*x^5+x^6)/(1-x)^8. - Vincenzo Librandi, Dec 10 2014

E.g.f.: (x/2)*(2 +63*x +301*x^2 +350*x^3 +140*x^4 +21*x^5 +x^6)*exp(x). - G. C. Greubel, Jan 12 2023

Extensions

More terms from Vincenzo Librandi, Dec 10 2014