OFFSET
0,3
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 77*x^5 + 272*x^6 + 954*x^7 +...
Related expansions:
A(x)^2 = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 202*x^5 + 779*x^6 + 2900*x^7 +...
A(x)^3 = 1 + 3*x + 9*x^2 + 28*x^3 + 90*x^4 + 402*x^5 + 1631*x^6 + 6372*x^7 +...
A(x)*A(-x) = 1 + 3*x^2 + 22*x^4 + 421*x^6 + 5386*x^8 + 127595*x^10 +...
A(x)*A(-x)*A(I*x)*A(-I*x) = 1 + 35*x^4 + 8730*x^8 + 3122301*x^12 + 1308019950*x^16 + 599139933987*x^20 + 290661820794000*x^24 +...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x*A^3*subst(A, x, -x)*subst(A, x, I*x)*subst(A, x, -I*x)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 14 2012
STATUS
approved