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A259607
G.f. satisfies: A(x) = 1+x + x^2 * A'(x)^2 / A(x)^2.
2
1, 1, 1, 2, 9, 66, 646, 7760, 109585, 1771810, 32211854, 649833996, 14399543754, 347618918364, 9080945744920, 255239884317292, 7680997048377377, 246417820289930866, 8395878803694101510, 302786064773642534220, 11523127939987785101646, 461518291638811484923036
OFFSET
0,4
LINKS
FORMULA
a(n) ~ c * 2^n * (n-1)!, where c = 0.09202081821632249728460... . - Vaclav Kotesovec, Jul 10 2015
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 9*x^4 + 66*x^5 + 646*x^6 + 7760*x^7 +...
The logarithmic derivative begins:
A'(x)/A(x) = 1 + x + 4*x^2 + 29*x^3 + 286*x^4 + 3478*x^5 + 49750*x^6 + 813949*x^7 +...+ A182356(n)*x^n +...
where
A'(x)^2/A(x)^2 = 1 + 2*x + 9*x^2 + 66*x^3 + 646*x^4 + 7760*x^5 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x + x^2*(A')^2/A^2 +x*O(x^n)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
Cf. A182356.
Sequence in context: A228696 A042255 A152213 * A214930 A089471 A196193
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 05 2015
STATUS
approved