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A168029
a(n) = n*(n^6 + 1)/2.
4
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
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: A144500 A374256 A086021 * A219413 A069424 A264268
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 11 2009
EXTENSIONS
More terms from Vincenzo Librandi, Dec 10 2014
STATUS
approved