A167963 a(n) = n*(n^5 + 1)/2.

0, 1, 33, 366, 2050, 7815, 23331, 58828, 131076, 265725, 500005, 885786, 1492998, 2413411, 3764775, 5695320, 8388616, 12068793, 17006121, 23522950, 32000010, 42883071, 56689963, 74017956, 95551500, 122070325, 154457901, 193710258, 240945166, 297411675

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 (7,-21,35,-35,21,-7,1).

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), this sequence (m=5), A168029 (m=6), A168067 (m=7), A168116 (m=8), A168118 (m=9), A168119 (m=10).

Programs

Magma

[n*(n^5+1)/2: n in [0..40]]; // Vincenzo Librandi, Dec 10 2014

Maple

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

Mathematica

Table[n(n^5+1)/2, {n,0,100}] (* Wesley Ivan Hurt, Nov 23 2013 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,33,366,2050,7815,23331},30] (* Harvey P. Dale, Dec 09 2014 *)
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 *)

SageMath

[n*(n^5+1)/2 for n in range(41)] # G. C. Greubel, Jan 17 2023

Formula

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

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