OFFSET
0,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..3000
FORMULA
EXAMPLE
G.f.: A(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 32*x^4 + 76*x^5 + 192*x^6 + 496*x^7 + 1332*x^8 + 3184*x^9 + 7920*x^10 + 19776*x^11 + 50432*x^12 +...
where
sqrt(A(x)) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 20*x^5 + 48*x^6 + 120*x^7 + 320*x^8 + 640*x^9 + 1520*x^10 + 3648*x^11 + 9216*x^12 +...+ A265264(n)*x^n +...
Illustration of initial terms:
PROG
(PARI) {a(n) = my(A=1+x); for(k=2, n, A = A + a((k+1)\2) * polcoeff(A^2, k\2) * x^k +x*O(x^n) ); polcoeff(A^2, n)}
for(n=0, 40, print1(a(n), ", "))
(PARI) {a(n) = my(A=[1, 1]); for(k=2, n, A = concat(A, A[(k+1)\2+1]*Vec(Ser(A)^2)[k\2+1]) ); Vec(Ser(A)^2)[n+1]}
for(n=0, 40, print1(a(n), ", "))
(PARI) /* Generates N terms rather quickly: */
N=300; A=[1, 1]; for(k=2, N, A = concat(A, A[(k+1)\2+1]*Vec(Ser(A)^2)[k\2+1]) ); Vec(Ser(A)^2)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 15 2015
STATUS
approved