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.

A054777 a(n) = 4*n*(4*n-1)*(4*n-2)*(4*n-3).

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%I A054777 #37 Mar 08 2022 05:09:23
%S A054777 0,24,1680,11880,43680,116280,255024,491400,863040,1413720,2193360,
%T A054777 3258024,4669920,6497400,8814960,11703240,15249024,19545240,24690960,
%U A054777 30791400,37957920,46308024,55965360,67059720,79727040,94109400,110355024,128618280,149059680,171845880
%N A054777 a(n) = 4*n*(4*n-1)*(4*n-2)*(4*n-3).
%D A054777 L. B. W. Jolley, Summation of Series, Dover, 1961.
%D A054777 Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 268.
%H A054777 Vincenzo Librandi, <a href="/A054777/b054777.txt">Table of n, a(n) for n = 0..10000</a>
%H A054777 Konrad Knopp, <a href="http://www.hti.umich.edu/cgi/t/text/text-idx?sid=b88432273f115fb346725f1a42422e19;c=umhistmath;idno=ACM1954.0001.001">Theorie und Anwendung der unendlichen Reihen</a>, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
%H A054777 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A054777 a(n) = A052762(4n) = 24*A060541(n).
%F A054777 Sum_{n>=1} 1/a(n) = log(2)/4 - Pi/24 = 0.0423871012404116... [Jolley eq. 242] - _Benoit Cloitre_, Apr 05 2002
%F A054777 G.f. -24*x*(1 + 65*x + 155*x^2 + 35*x^3) / (x-1)^5. - _R. J. Mathar_, Oct 03 2011
%F A054777 Sum_{n>=1} (-1)^(n+1)/a(n) = log(sqrt(2)-1)/(6*sqrt(2)) - log(2)/24 + (1/(6*sqrt(2)) - 1/16)*Pi. - _Amiram Eldar_, Mar 08 2022
%t A054777 a[n_] := 4*n*(4*n-1)*(4*n-2)*(4*n-3); Array[a, 40, 0] (* _Amiram Eldar_, Mar 08 2022 *)
%o A054777 (Magma) [4*n*(4*n-1)*(4*n-2)*(4*n-3): n in [0..30]]; // _Vincenzo Librandi_, Oct 04 2011
%Y A054777 Cf. A052762, A060541, A104188.
%K A054777 easy,nonn
%O A054777 0,2
%A A054777 _Henry Bottomley_, May 19 2000