OFFSET
1,6
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..100
FORMULA
G.f. A(x) satisfies: A(-A(-x)) = x.
EXAMPLE
G.f.: A(x) = x + x^2 + x^3 + x^4 + x^5 + 6*x^6 + 21*x^7 + 68*x^8 + 186*x^9 + 495*x^10 + 1335*x^11 + 3744*x^12 + 10870*x^13 + 32120*x^14 + 95565*x^15 + ...
such that
1 = 1 - (x - A(x)) + (x + A(x)^2)*(x^2 - A(x)) - (x - A(x)^3)*(x^2 + A(x)^2)*(x^3 - A(x)) + (x + A(x)^4)*(x^2 - A(x)^3)*(x^3 + A(x)^2)*(x^4 - A(x)) - (x - A(x)^5)*(x^2 + A(x)^4)*(x^3 - A(x)^3)*(x^4 + A(x)^2)*(x^5 - A(x)) + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = -Vec( sum(m=0, #A, (-1)^m * prod(k=1, m, x^(m+1-k) + (-x)^k*Ser(A)^k ) ) )[#A+1]); A[n]}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 21 2018
STATUS
approved