cp's OEIS Frontend

A086602 a(n) = A000217(A000217(n))-n^2.

%I A086602 #36 Apr 04 2023 10:53:00
%S A086602 0,0,2,12,39,95,195,357,602,954,1440,2090,2937,4017,5369,7035,9060,
%T A086602 11492,14382,17784,21755,26355,31647,37697,44574,52350,61100,70902,
%U A086602 81837,93989,107445,122295,138632,156552,176154,197540,220815,246087
%N A086602 a(n) = A000217(A000217(n))-n^2.
%H A086602 Q. T. Bach, R. Paudyal, J. B. Remmel, <a href="https://arxiv.org/abs/1510.04310">A Fibonacci analogue of Stirling numbers</a>, arXiv preprint arXiv:1510.04310 [math.CO], 2015-2016.
%H A086602 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A086602 a(n) = A000330(n-1)+A001295(n-1). - _Alford Arnold_, Jun 29 2005
%F A086602 a(n) = 3*C(n+2,4) - C(n,2). - _Zerinvary Lajos_, May 02 2007, corrected Jun 12 2018
%F A086602 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) = n*(n-1)*(n^2+3*n-2)/8. [_R. J. Mathar_, Oct 30 2009]
%F A086602 G.f.: x^2*(-2-2*x+x^2)/(x-1)^5. [_R. J. Mathar_, Oct 30 2009]
%F A086602 a(n) = (n-1)*A005581(n) - Sum_{i=0..n-1} A005581(i). [_Bruno Berselli_, Aug 27 2014]
%e A086602 a(3) = t(t(3))-3^2 = t(6)-9 = 21-9 = 12.
%p A086602 seq(3*binomial(n+2,4)-binomial(n,2), n=0..35); # _Zerinvary Lajos_, May 02 2007
%t A086602 Table[n (n - 1) (n^2 + 3 n - 2)/8, {n, 0, 40}] (* _Bruno Berselli_, Aug 27 2014 *)
%t A086602 LinearRecurrence[{5,-10,10,-5,1},{0,0,2,12,39},60] (* _Harvey P. Dale_, Apr 04 2023 *)
%o A086602 (PARI) t(i)=i*(i+1)/2
%o A086602 vector(40,i,t(t(i))-i^2)
%o A086602 (Magma) [n*(n-1)*(n^2+3*n-2)/8: n in [0..40]]; // _Vincenzo Librandi_, Jun 26 2016
%Y A086602 Cf. A000330, A001296, A005581.
%K A086602 nonn,easy
%O A086602 0,3
%A A086602 _Jon Perry_, Jul 23 2003