A067145 Shifts left under reversion.
1, 1, -1, 3, -13, 69, -419, 2809, -20353, 157199, -1281993, 10963825, -97828031, 907177801, -8716049417, 86553001779, -886573220093, 9351927111901, -101447092428243, 1130357986741545, -12923637003161409, 151479552582252239, -1818756036793636033
Offset: 1
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..200
- N. J. A. Sloane, Transforms
Crossrefs
Cf. A107094.
Apart from signs, same as A088714. - Philippe Deléham, Jun 18 2006
Programs
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Mathematica
Nest[InverseSeries[#] x + x &, x + O[x]^2, 50][[3]] (* Vladimir Reshetnikov, Aug 07 2019 *)
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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 */
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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 */
Formula
G.f. satisfies A^(-1)(x) = A(x)/x - 1.
G.f. satisfies: A(A(x)) = (1+x)*A(x) = g.f. of A107094. - Paul D. Hanna, May 12 2005
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
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
Comments