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%I #10 Jan 16 2019 18:39:42
%S 1,-3,5,77,277,140173,1743859,2076083,259374867533,57573296785133,
%T 770098483166113,5605884055023955789,7228014618092706553,
%U 3332173791979508526419,27269879914911094298619533,91854722122840672285969818121,10712330835046717680588811970893,283551664519128905300910019306673
%N Numerators of the sequence c(n) satisfying Sum_{k=0..n} c(k)/(n+k+1) = 0 with c(0)=1.
%H Alexander Kalmynin, Petr Kosenko, <a href="https://arxiv.org/abs/1901.04044">Orthorecursive expansion of unity</a>, arXiv:1901.04044 [math.NT], 2019.
%e The sequence c(n) begins: 1, -3/2, 5/24, 77/720, 277/4480, 140173/3628800, ...
%o (PARI) lista(nn) = {my(c0 = 1, vc = vector(nn)); for (n=1, nn, vc[n] = -(2*n+1)*(c0/(n+1) + sum(k=1, n-1, vc[k]/(n+k+1)));); apply(x->numerator(x), concat([c0], vc));}
%Y Cf. A323491 (denominators), A323492 (sign changes).
%K sign,frac
%O 0,2
%A _Michel Marcus_, Jan 16 2019
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