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.
%I A224270 #34 Oct 13 2024 11:31:02
%S A224270 1,1,5,11,95,203,861,1815,30459,63635,264979,550069,4555915,9412543,
%T A224270 38816525,79898895,2627302995,5392044675,22104436695,45256266825,
%U A224270 370241638305,756514878405,3088866211275,6300861570705,102746354288175,209286947903319
%N A224270 Absolute values of the numerators of the third column of ( 0 followed by (interleave 0 , A001803(n))/A060818(n) ) and its successive differences.
%C A224270 The array is
%C A224270 0, 0, 1, 0, 3/2, 0, 15/8, 0,...
%C A224270 0, 1, -1, 3/2, -3/2, 15/8, -15/8,...
%C A224270 1, -2, 5/2, -3, 27/8, -15/4,...
%C A224270 -3, 9/2, -11/2, 51/8, -57/8,...
%C A224270 15/2, -10, 95/8, -27/2,...
%C A224270 -35/2, 175/8, -203/8,...
%C A224270 315/8, -189/4,...
%C A224270 -693/8,...
%C A224270 Note A001803 in the first column and a variant of A206771(n) in the second column.
%C A224270 Now consider a(n)/A046161(n) and its differences:
%C A224270 1, 1/2, 5/8, 11/16, 95/128, 203/256, 861/1024,...
%C A224270 -1/2, 1/8, 1/16, 7/128, 13/256, 49/1024,... =b(n)/A046161(n)
%C A224270 5/8, -1/16, -1/128, -1/256, -3/1024,...
%C A224270 -11/16, 7/128, 1/256, 1/1024,...
%C A224270 95/128, -13/256, -3/1024,...
%C A224270 -203/256, 49/1024,...
%C A224270 861/1024,...
%C A224270 This an autosequence of second kind. The first column is the signed sequence.
%C A224270 (Its companion, the corresponding autosequence of first kind, is 0, 1, 1, 9/8, 5/4,... in A206771).
%C A224270 Main diagonal: 1, 1/8, -1/128,... = A002596(n)/A061549(n) ?
%C A224270 b(n) = a(n+1) - A171977*a(n). Also for two successive rows (with shifted A171977).
%H A224270 Vincenzo Librandi, <a href="/A224270/b224270.txt">Table of n, a(n) for n = 0..200</a>
%F A224270 Numerators of (0, 0 followed by A001803(n)/(4*A046161(n))) + A001790(n)/A046161(n).
%e A224270 a(n)=numerators of 0+1=1, 0+1/2=1/2, 1/4+3/8=5/8, 3/8+5/16=11/16, 15/32+35/128=95/128,... .
%t A224270 nmax = 25; t1 = Table[ Numerator[ (2*n+1)*(Binomial[2*n, n]/4^n)] / Denominator[ Binomial[2*n, n]/4^n], {n, 0, Ceiling[nmax/2]}]; t2 = Join[{0}, Table[ If[ OddQ[n], 0, t1[[n/2]] ], {n, 1, nmax+2}] ]; t3 = Table[ Differences[t2, n], {n, 0, nmax}]; t3[[All, 3]] // Numerator // Abs (* _Jean-François Alcover_, Apr 02 2013 *)
%Y A224270 Cf. A001790, A001803, A002596, A046161, A061549, A098597, A171977, A206771.
%K A224270 nonn,frac,less
%O A224270 0,3
%A A224270 _Paul Curtz_, Apr 02 2013
%E A224270 More terms from _Jean-François Alcover_, Apr 02 2013