OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
FORMULA
G.f. satisfies: A(x) = (1 - 2*x*A(x^2) - sqrt(1 - 4*x*A(x^2))) / (2*x^2).
Equals the self-convolution square of A182144, where
a(2*n) = A182144(2*n+1) for n>=0,
a(2*n-1) = A182144(2*n) - a(n) for n>0 with a(0)=1.
a(n) ~ c * d^n / n^(3/2), where d = 4.498712103893737093320276... (same as for A182144), c = 3.2247879599569180737223... . - Vaclav Kotesovec, Aug 08 2014
EXAMPLE
G.f.: A(x) = 1 + 2*x + 9*x^2 + 26*x^3 + 104*x^4 + 350*x^5 + 1321*x^6 +...
The square-root of the g.f. yields the g.f. of A182144:
A(x)^(1/2) = 1 + x + 4*x^2 + 9*x^3 + 35*x^4 + 104*x^5 + 376*x^6 + 1321*x^7 + 4960*x^8 + 18667*x^9 + 72220*x^10 + 282368*x^11 + 1119791*x^12 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=(subst(A, x, x^2+x*O(x^n))+x*A)^2); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 24 2012
STATUS
approved