OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation A^{2^n}(x)=F(x), arXiv:1302.1986 [math.CO], 2013.
FORMULA
a(n) = T(n,1), T(n,k) = 1 if n=k, else T(n,k) = 1/2*((sum(i=k..n, C(i-1,k-1) * C(i,n-i))) * 2^(n-k) - sum(i=k+1..n-1, T(n,i)*T(i,k))).
MAPLE
a:= n-> T(n, 1):
T:= proc(n, k) option remember;
`if`(n=k, 1, (add(binomial(i-1, k-1) *binomial(i, n-i), i=k..n)
*2^(n-k) -add(T(n, i)*T(i, k), i=k+1..n-1))/2)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Nov 11 2011
MATHEMATICA
a[n_] := T[n, 1]; T[n_, k_] := T[n, k] = If[n == k, 1, 1/2*(Sum[Binomial[i-1, k-1] * Binomial[i, n-i], {i, k, n}]*2^(n-k) - Sum[T[n, i]*T[i, k], {i, k+1, n-1}]) ]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 21 2015, from formula *)
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Nov 11 2011
STATUS
approved