OFFSET
1,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..552
Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation $A^{2^n}(x)=F(x)$, arXiv:1302.1986
FORMULA
a(n)=T(n,1), 2*T(n,m)= 2^(n-m) *sum_{j=0..m} binomial(j,n-3*m+2*j) *binomial(m,j) -sum_{k=m+1..n-1} T(n,k)*T(k,m), n>m, T(n,n)=1.
EXAMPLE
First column of
1;
1,1;
1,2,1;
-3,3,3,1;
5,-4,6,4,1;
1,5,-2,10,5,1;
-39,6,3,4,15,6,1;
117,-57,9,3,15,21,7,1;
13,128,-56,8,10,32,28,8,1;
-1311,201,84,-44,6,30,56,36,9,1;
MATHEMATICA
t[n_, m_] := t[n, m] = 1/2*(2^(n-m)*Sum[Binomial[j, n - 3*m + 2*j]*Binomial[m, j], {j, 0, m}] - Sum[t[n, k]*t[k, m], {k, m+1, n-1}]); t[n_, n_] = 1; Table[t[n, 1], {n, 1, 27}] (* Jean-François Alcover, Feb 22 2013 *)
PROG
(Maxima)
T(n, m):=if n=m then 1 else 1/2*(2^(n-m)*sum(binomial(j, n-3*m+2*j)*binomial(m, j), j, 0, m)-sum(T(n, k)*T(k, m), k, m+1, n-1));
makelist((T(n, 1)), n, 1, 10);
CROSSREFS
KEYWORD
sign
AUTHOR
Dmitry Kruchinin, Dec 05 2012
STATUS
approved