A168119 -id:A168119 - cp's OEIS frontend

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

N. J. A. Sloane, Dec 11 2009

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).

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).

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

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 *)

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

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

More terms from Vincenzo Librandi, Dec 10 2014

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

Original entry on oeis.org

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

N. J. A. Sloane, Dec 11 2009

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).

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).

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

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

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 *)

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

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

cp's OEIS Frontend

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

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