OFFSET
1,2
COMMENTS
FORMULA
Sum_{n>=1} a(n)/8^n = 1/2.
EXAMPLE
G.f. A(x) = x + 8*x^2 + 46*x^3 + 256*x^4 + 1286*x^5 + 6400*x^6 + 30348*x^7 + 142352*x^8 + 652486*x^9 + 2958864*x^10 + ...
Specific values.
A(1/8) = 1/2 = 1/8 + 8/8^2 + 46/8^3 + 256/8^4 + 1286/8^5 + 6400/8^6 + ...
PROG
(PARI) {a(n) = my(A, P = -y + x*O(x^(2*n+1)));
for(i=1, n+1, P = sqrt(1 - 4*x + 4*x*P +x*O(x^(2*n+1))); );
A = subst(derivn( (1 - P)/(2*x)^(n+1) , 2, y)/2, y, 0); polcoeff(A, n, x)}
for(n=1, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 05 2022
STATUS
approved