OFFSET
0,2
COMMENTS
Essentially an unsigned version of A352705 (after dropping the initial term).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..1000
FORMULA
G.f. A(x) satisfies:
(1) (1 + x*A(-x))^7 = 1 + 7*x + x^7*A(-x^7).
(2) A(x) = (1 - (1 - 7*x - x^7*A(x^7))^(1/7))/x.
(3) A(x)^7 = A(x^7) (mod 7).
EXAMPLE
G.f.: A(x) = 1 + 3*x + 13*x^2 + 65*x^3 + 351*x^4 + 1989*x^5 + 11650*x^6 + 69900*x^7 + 427167*x^8 + 2648438*x^9 + 16612947*x^10 + ...
where
(1 - x*A(x))^7 = 1 - 7*x - x^7 - 3*x^14 - 13*x^21 - 65*x^28 - 351*x^35 - 1989*x^42 - 11650*x^49 - 69900*x^56 - 427167*x^63 - 2648438*x^70 + ...
also
(1 - 7*x - x^7*A(x^7))^(1/7) = 1 - x - 3*x^2 - 13*x^3 - 65*x^4 - 351*x^5 - 1989*x^6 - 11650*x^7 - 69900*x^8 - 427167*x^9 - 2648438*x^10 + ...
which equals 1 - x*A(x).
PROG
(PARI) {a(n) = my(A=1+3*x); for(i=1, n,
A = (1 - (1 - 7*x - x^7*subst(A, x, x^7) + x*O(x^(n+1)))^(1/7))/x);
polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 29 2022
STATUS
approved