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%I #28 Aug 09 2019 02:59:44
%S 1,1,-1,3,-13,69,-419,2809,-20353,157199,-1281993,10963825,-97828031,
%T 907177801,-8716049417,86553001779,-886573220093,9351927111901,
%U -101447092428243,1130357986741545,-12923637003161409,151479552582252239,-1818756036793636033
%N Shifts left under reversion.
%H Alois P. Heinz, <a href="/A067145/b067145.txt">Table of n, a(n) for n = 1..200</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F G.f. satisfies A^(-1)(x) = A(x)/x - 1.
%F G.f. satisfies: A(A(x)) = (1+x)*A(x) = g.f. of A107094. - _Paul D. Hanna_, May 12 2005
%F G.f. A(x) satisfies 0=f(x, A(x), A(A(x))) where f(a0,a1,a2) = a1 - a2 + a0*a1. - _Michael Somos_, May 21 2005
%F a(n) = T(n-1,1), n > 1, a(1) = 1, T(n,m) = (m/n) * Sum_{k=1..n-m} T(n-m,k) * (-1)^k * binomial(k+n-1, n-1), n > m, T(n,n) = 1. - _Vladimir Kruchinin_, May 06 2012
%t Nest[InverseSeries[#] x + x &, x + O[x]^2, 50][[3]] (* _Vladimir Reshetnikov_, Aug 07 2019 *)
%o (PARI) {a(n)=local(A); if(n<1, 0, A=x+O(x^2); for(i=2,n, A=x*(1+serreverse(A))); polcoeff(A,n))} /* _Michael Somos_, May 21 2005 */
%o (Maxima) T(n,m):=if n=m then 1 else m/n*sum(T(n-m,k)*(-1)^k*binomial(k+n-1,n-1), k,1,n-m); a(n):=if n=1 then 1 else T(n-1,1); [_Vladimir Kruchinin_, May 06 2012]
%Y Cf. A107094.
%Y Apart from signs, same as A088714. - _Philippe Deléham_, Jun 18 2006
%Y Cf. A309254, A309564.
%K sign,eigen
%O 1,4
%A _Christian G. Bower_, Jan 03 2002
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