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 A067145 #31 Nov 16 2024 12:17:20
%S A067145 1,1,-1,3,-13,69,-419,2809,-20353,157199,-1281993,10963825,-97828031,
%T A067145 907177801,-8716049417,86553001779,-886573220093,9351927111901,
%U A067145 -101447092428243,1130357986741545,-12923637003161409,151479552582252239,-1818756036793636033
%N A067145 Shifts left under reversion.
%H A067145 Alois P. Heinz, <a href="/A067145/b067145.txt">Table of n, a(n) for n = 1..200</a>
%H A067145 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A067145 G.f. satisfies A^(-1)(x) = A(x)/x - 1.
%F A067145 G.f. satisfies: A(A(x)) = (1+x)*A(x) = g.f. of A107094. - _Paul D. Hanna_, May 12 2005
%F A067145 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 A067145 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 A067145 Nest[InverseSeries[#] x + x &, x + O[x]^2, 50][[3]] (* _Vladimir Reshetnikov_, Aug 07 2019 *)
%o A067145 (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 A067145 (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 A067145 Cf. A107094.
%Y A067145 Apart from signs, same as A088714. - _Philippe Deléham_, Jun 18 2006
%Y A067145 Cf. A309254, A309564.
%K A067145 sign,eigen
%O A067145 1,4
%A A067145 _Christian G. Bower_, Jan 03 2002