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

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

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

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 *)

Prog

(Magma) [n*(n^6+1)/2: n in [0..40]]; // Vincenzo Librandi, Dec 10 2014
(SageMath) [n*(n^6+1)/2 for n in range(41)] # G. C. Greubel, Jan 12 2023

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).

Sequence in context: A279639 A144500 A086021 * A219413 A069424 A264268

Adjacent sequences: A168026 A168027 A168028 * A168030 A168031 A168032

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 2009

Extensions

More terms from Vincenzo Librandi, Dec 10 2014

Status

approved