A185168 G.f. A(x) where A000081(x) = x*A(A000081(x)).

1, 1, 1, 0, 0, -1, 3, -5, 7, -8, 1, 24, -62, 82, -60, 52, -242, 877, -1979, 2747, -924, -7309, 28389, -79469, 205108, -468281, 821680, -772531, -1046280, 6962678, -19516746, 39741239, -63920180, 75119743, -21689924, -219360085, 866264658, -2165202646, 4125523796, -6023253532

Offset: 0

Author

Vladimir Kruchinin, Feb 19 2011

Keywords

• sign

Links

• Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Programs

Mathematica

m = maxExponent = 31;
A81[] = 0; Do[A81[x] = x*Exp[Sum[A81[x^k]/k, {k, 1, m}] + O[x]^m] // Normal, {m}];
A[x_] = Sum[a[k] x^k, {k, 0, m}];
cc = CoefficientList[A81[x] - x A[A81[x]] + O[x]^m, x];
Table[a[n], {n, 0, m-2}] /. Solve[Thread[cc == 0]] // First (* Jean-François Alcover, Aug 08 2018 *)