cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A086755 Sum_{k=1..n} (k(k+1))^2/2.

This page as a plain text file.
%I A086755 #13 Oct 04 2020 16:40:55
%S A086755 2,20,92,292,742,1624,3192,5784,9834,15884,24596,36764,53326,75376,
%T A086755 104176,141168,187986,246468,318668,406868,513590,641608,793960,
%U A086755 973960,1185210,1431612,1717380,2047052,2425502,2857952,3349984,3907552
%N A086755 Sum_{k=1..n} (k(k+1))^2/2.
%H A086755 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A086755 (n+1)(n+2)(n+3)(3n^2+12n+10)/30 = 2*A024166(n+1).
%F A086755 G.f. 2*(1+4*x+x^2) / (x-1)^6 . - _R. J. Mathar_, Sep 15 2012
%e A086755 a(3)=(1*2)^2/2+(2*3)^2/2+(3.4)^2/2=2+18+72=92
%t A086755 Table[Sum[(k(k+1))^2/2,{k,n}],{n,40}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{2,20,92,292,742,1624},40] (* _Harvey P. Dale_, Oct 04 2020 *)
%o A086755 (PARI) for(i=1,20,print1(","sum(j=1,i,(j*(j+1))^2/2)))
%K A086755 nonn,easy
%O A086755 0,1
%A A086755 _Jon Perry_, Jul 31 2003
%E A086755 More terms from _Jason Earls_, Aug 01 2003
%E A086755 Definition clarified by _Harvey P. Dale_, Oct 04 2020