A152725 a(n) = n*(n+1)*(n^4 + 2*n^3 - 2*n^2 - 3*n + 3)/2.

0, 1, 63, 666, 3430, 12195, 34461, 83188, 178956, 352485, 647515, 1124046, 1861938, 2964871, 4564665, 6825960, 9951256, 14186313, 19825911, 27219970, 36780030, 48986091, 64393813, 83642076, 107460900, 136679725, 172236051, 215184438

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A062392, A062393 (for 5th powers), A011934, A152726 (for 7th powers).

Programs

Magma

[n*(n+1)*(n^4+2*n^3-2*n^2-3*n+3)/2: n in [0..50]]; // G. C. Greubel, Sep 01 2018

Mathematica

k=0;lst={k};Do[k=n^6-k;AppendTo[lst,k],{n,1,5!}];lst
LinearRecurrence[{7,-21,35,-35,21,-7,1}, {0,1,63,666,3430,12195,34461}, 50] (* G. C. Greubel, Sep 01 2018 *)
CoefficientList[Series[-((x (1+56 x+246 x^2+56 x^3+x^4))/(-1+x)^7),{x,0,30}],x] (* Harvey P. Dale, Aug 03 2024 *)

PARI

a(n)=n*(n+1)*(n^4+2*n^3-2*n^2-3*n+3)/2 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = n^6 - (n-1)^6 + (n-2)^6 - ... + ((-1)^n)*0^6.

G.f.: x*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1-x)^7. - R. J. Mathar, Jul 08 2013

a(n) = A050492(A000217(n)). - Kelvin Voskuijl, Jun 18 2025

E.g.f.: exp(x)*x*(2 + 61*x + 160*x^2 + 95*x^3 + 18*x^4 + x^5)/2. - Stefano Spezia, Jun 19 2025

Extensions

Offset set to 0 by R. J. Mathar, Aug 15 2010