A167963 - OEIS

%I #25 Jan 18 2023 02:21:29

%S 0,1,33,366,2050,7815,23331,58828,131076,265725,500005,885786,1492998,

%T 2413411,3764775,5695320,8388616,12068793,17006121,23522950,32000010,

%U 42883071,56689963,74017956,95551500,122070325,154457901,193710258,240945166,297411675

%N a(n) = n*(n^5 + 1)/2.

%H Vincenzo Librandi, <a href="/A167963/b167963.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F G.f.: x*(1 + 26*x + 156*x^2 + 146*x^3 + 31*x^4)/(1-x)^7. - _Vincenzo Librandi_, Dec 10 2014

%F E.g.f.: (1/2)*x*(2 + 31*x + 90*x^2 + 65*x^3 + 15*x^4 + x^5)*exp(x). - _G. C. Greubel_, Jan 17 2023

%p A167963:=n->n*(n^5+1)/2; seq(A167963(n), n=0..100); # _Wesley Ivan Hurt_, Nov 23 2013

%t Table[n(n^5+1)/2, {n,0,100}] (* _Wesley Ivan Hurt_, Nov 23 2013 *)

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,33,366,2050,7815,23331},30] (* _Harvey P. Dale_, Dec 09 2014 *)

%t CoefficientList[Series[x (1 + 26 x + 156 x^2 + 146 x^3 + 31 x^4) / (1 - x)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 10 2014 *)

%o (Magma) [n*(n^5+1)/2: n in [0..40]]; // _Vincenzo Librandi_, Dec 10 2014

%o (SageMath) [n*(n^5+1)/2 for n in range(41)] # _G. C. Greubel_, Jan 17 2023

%Y Sequences of the form n*(n^m + 1)/2: A001477 (m=0), A000217 (m=1), A006003 (m=2), A027441 (m=3), A021003 (m=4), this sequence (m=5), A168029 (m=6), A168067 (m=7), A168116 (m=8), A168118 (m=9), A168119 (m=10).

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 11 2009