OFFSET
0,3
COMMENTS
More generally, we have the identity for real t:
* if G(x) = exp( Integral G(x)^t * Integral 1/G(x)^(3*t) dx dx ),
then G(x) = exp( Integral 1/G(x)^t * Integral G(x)^(3*t) dx dx ).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..180
FORMULA
E.g.f. A(x) satisfies: A(x) = exp( Integral 1/A(x)^3 * Integral A(x)^9 dx dx ).
EXAMPLE
E.g.f. A(x) = 1 + x^2/2! + 3*x^4/4! + 123*x^6/6! + 3129*x^8/8! + 313929*x^10/10! +...
PROG
(PARI) {a(n) = local(A=1+x); for(i=1, n, A = exp( intformal( A^3 * intformal(1/A^9 + x*O(x^n)) ) ) ); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(2*n), ", "))
(PARI) {a(n) = local(A=1+x); for(i=1, n, A = exp( intformal( 1/A^3 * intformal(A^9 + x*O(x^n)) ) ) ); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(2*n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 06 2015
STATUS
approved