A091138 E.g.f. A(x) satisfies A(A(x)) = x/(1-x)^2.

1, 2, 3, 6, 15, 0, 315, 1890, -82215, 708750, 41008275, -1385549550, -33403344975, 3426898600125, 26529571443375, -13516476003780750, 157765729690193625, 84230651703487038750, -3280917943856839411125, -799561865724400084556250, 62859004972802312944044375

Offset: 1

Author

Vladeta Jovovic, Dec 20 2003

Keywords

• easy
• frac
• fini
• sign

Comments

First non-integer term is a(30) = 16103946844555056574100466078211185438823359375/2.

Links

• R. J. Mathar, Table of n, a(n) for n = 1..28
• Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation A^{2^n}(x)=F(x), arXiv:1302.1986

Programs

Mathematica

t[n_, m_] := t[n, m] = If[n == m, 1, 1/2*(Binomial[n+m-1, 2*m-1] - Sum[t[n, i]*t[i, m], {i, m+1, n-1}])]; a[n_] := n!*t[n, 1]; Table[a[n], {n, 1, 21}] (* Jean-François Alcover, Feb 26 2013, after Vladimir Kruchinin *)

Maxima

T(n,m):=if n=m then 1 else 1/2*(binomial(n+m-1,2*m-1)-sum(T(n,i)*T(i,m),i,m+1,n-1));
makelist(2^(n-1)*T(n,1),n,1,10); /* Vladimir Kruchinin, Mar 14 2012 */

Formula

a(n) = n!* A030274(n)/A030275(n).

a(n) = n!*T(n,1), T(n,m)=1/2*(binomial(n+m-1,2*m-1)-sum(i=m+1..n-1, T(n,i)*T(i,m))), n>m, T(n,n)=1. - Vladimir Kruchinin, Mar 14 2012

Extensions

More terms from R. J. Mathar, Apr 28 2007