OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
G.f.: A(x) = 1/(1 - A(x/(1-x))^2*x/(1-x) ).
MAPLE
bintr:= proc(p) local b; b:= proc(n) option remember;
add(p(k) *binomial(n, k), k=0..n) end
end:
invtr:= proc(p) local b; b:= proc(n) option remember;
`if`(n<1, 1, add(b(n-i) *p(i-1), i=1..n+1)) end
end:
b:= invtr(bintr(n-> add(a(i)*a(n-i), i=0..n))):
a:= n-> `if`(n<0, 0, b(n-1)):
seq(a(n), n=0..30); # Alois P. Heinz, Jun 28 2012
MATHEMATICA
m = 30; A[_] = 1; Do[A[x_] = 1/(1 - A[x/(1-x)]^2*(x/(1-x))) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Jun 04 2018 *)
PROG
(PARI) {a(n)=local(A); if(n<0, 0, A=1+x+x*O(x^n); for(k=1, n, B=subst(A^2, x, x/(1-x))/(1-x)+x*O(x^n); A=1+x*A*B); polcoeff(A, n, x))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 26 2003
STATUS
approved