A030180 a(n) = (n^7 - n)/42.

0, 0, 3, 52, 390, 1860, 6665, 19608, 49932, 113880, 238095, 463980, 853138, 1494012, 2509845, 4068080, 6391320, 9769968, 14576667, 21282660, 30476190, 42883060, 59389473, 81067272, 109201700, 145321800, 191233575, 249056028, 321260202, 410711340, 520714285

Offset: 0

Author

Charlton Harrison (charlton(AT)bach.dynet.com)

Keywords

• nonn

Links

• G. C. Greubel, 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).

Crossrefs

Cf. A133499 (n^7-n).

Programs

GAP

List([0..35], n-> (n^7-n)/42); # G. C. Greubel, Dec 28 2019

Magma

[(n^7-n)/42: n in [0..35]]; // G. C. Greubel, Dec 28 2019

Maple

seq( (n^7-n)/42, n=0..35); # G. C. Greubel, Dec 28 2019

Mathematica

Table[(n^7-n)/42, {n,0,35}] (* G. C. Greubel, Dec 28 2019 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,0,3,52,390,1860,6665,19608},40] (* Harvey P. Dale, May 14 2022 *)

PARI

a(n) = (n^7-n)/42; \\ Michel Marcus, Aug 30 2013

Sage

[(n^7-n)/42 for n in (0..35)] # G. C. Greubel, Dec 28 2019

Formula

a(n) = A133499(n)/42. - Michel Marcus, Aug 30 2013

From Stefano Spezia, Dec 29 2019: (Start)

O.g.f.: x^2*(3 + 28*x + 58*x^2 + 28*x^3 + 3*x^4)/(1 - x)^8.

E.g.f.: (1/42)*exp(x)*x^2*(63 + 301*x + 350*x^2 + 140*x^3 + 21*x^4 + x^5).

(End)