cp's OEIS Frontend

A178073 Partial sums of sequence A177342.

%I A178073 #20 Feb 02 2025 11:52:53
%S A178073 1,10,41,116,265,526,945,1576,2481,3730,5401,7580,10361,13846,18145,
%T A178073 23376,29665,37146,45961,56260,68201,81950,97681,115576,135825,158626,
%U A178073 184185,212716,244441,279590,318401,361120,408001,459306,515305
%N A178073 Partial sums of sequence A177342.
%C A178073 a(n)==1 (mod n+1). E.g., a(4)=116 and 116==1 (mod 5), a(11)=5401 and 5401==1 (mod 12).
%C A178073 Inverse binomial transform of this sequence: 1, 9, 22, 22, 8, 0, 0 (0 continued).
%H A178073 B. Berselli, <a href="/A178073/b178073.txt">Table of n, a(n) for n = 1..10000</a>.
%H A178073 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A178073 a(n) = n*(n^3+n^2+2*n-1)/3.
%F A178073 G.f.: x*(1+5*x+x^2+x^3)/(1-x)^5.
%F A178073 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) with n>5.
%F A178073 a(n)+a(-n) = A035598(n). [_Bruno Berselli_, Jun 21 2012]
%t A178073 LinearRecurrence[{5,-10,10,-5,1},{1,10,41,116,265},40] (* _Harvey P. Dale_, Feb 02 2025 *)
%o A178073 (Magma) A177342:=func<n | (4*n^3-3*n^2+5*n-3)/3>; [&+[A177342(i): i in [1..n]]: n in [1..35]]; // _Bruno Berselli_, Jun 21 2012
%K A178073 nonn,easy
%O A178073 1,2
%A A178073 _Bruno Berselli_, May 31 2010
%E A178073 Edited by _Bruno Berselli_, Dec 29 2010