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.

A026960 a(n) = Sum_{k=0..n} (k+1) * A026615(n,k).

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%I A026960 #19 Jun 17 2024 07:01:53
%S A026960 1,3,10,30,78,189,440,999,2230,4917,10740,23283,50162,107505,229360,
%T A026960 487407,1032174,2179053,4587500,9633771,20185066,42205161,88080360,
%U A026960 183500775,381681638,792723429,1644167140,3405774819,7046430690,14562623457,30064771040
%N A026960 a(n) = Sum_{k=0..n} (k+1) * A026615(n,k).
%H A026960 Colin Barker, <a href="/A026960/b026960.txt">Table of n, a(n) for n = 0..1000</a>
%H A026960 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F A026960 For n>1, a(n) = 7*(n+2)*2^(n-3) - n - 2.
%F A026960 From _Colin Barker_, Feb 18 2016: (Start)
%F A026960 a(n) = 6*a(n-1)-13*a(n-2)+12*a(n-3)-4*a(n-4) for n>5
%F A026960 G.f.: (1-3*x+5*x^2-3*x^3-4*x^4+3*x^5) / ((1-x)^2*(1-2*x)^2).
%F A026960 (End)
%t A026960 Join[{1,3},Table[7(n+2)2^(n-3)-n-2,{n,2,30}]] (* or *) LinearRecurrence[ {6,-13,12,-4},{1,3,10,30,78,189},30] (* _Harvey P. Dale_, Oct 31 2015 *)
%o A026960 (PARI) Vec((1-3*x+5*x^2-3*x^3-4*x^4+3*x^5)/((1-x)^2*(1-2*x)^2) + O(x^40)) \\ _Colin Barker_, Feb 18 2016
%o A026960 (Magma) [n le 1 select 2*n+1 else 7*(n+2)*2^(n-3) - n - 2: n in [0..40]]; // _G. C. Greubel_, Jun 16 2024
%o A026960 (SageMath) [7*(n+2)*2^(n-3) - n - 2 + (5/4)*int(n==0) + (3/4)*int(n==1) for n in range(41)] # _G. C. Greubel_, Jun 16 2024
%Y A026960 Cf. A026615, A026616, A026617, A026618, A026619, A026620, A026621.
%Y A026960 Cf. A026622, A026623, A026624, A026625, A026956, A026957, A026958.
%Y A026960 Cf. A026959.
%K A026960 nonn,easy
%O A026960 0,2
%A A026960 _Clark Kimberling_