OFFSET
0,4
FORMULA
E.g.f. satisfies: A(x) = B(x/A(x)) and A(x*B(x)) = B(x) where B(x) satisfies:
B(x) = Sum_{n>=0} x^n/n! * B(x)^(n*(n+1)/2) and is the e.g.f. of A155805.
EXAMPLE
E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 19*x^4/4! + 161*x^5/5! +...
where e.g.f. A(x) satisfies:
A(x) = 1 + x + x^2/2!*A(x) + x^3/3!*A(x)^3 + x^4/4!*A(x)^6 + x^5/5!*A(x)^10 +...
Let B(x) = A(x*B(x)) be the e.g.f. of A155805 then:
B(x) = 1 + x*B(x) + x^2/2!*B(x)^3 + x^3/3!*B(x)^6 + x^4/4!*B(x)^10 +...
B(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 191*x^4/4! + 2656*x^5/5! + 47392*x^6/6! +...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+sum(k=1, n, x^k*A^(k*(k-1)/2)/k!+x*O(x^n))); n!*polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 27 2009
STATUS
approved