A155806 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n^2).

1, 1, 3, 22, 269, 4616, 102847, 2824816, 92355769, 3506278528, 151720849691, 7375146930944, 398113181435653, 23640909385071616, 1532325553233566743, 107698939845869111296, 8162300091585206125553, 663836705760309127184384

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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)) and is the e.g.f. of A155807.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 269*x^4/4! + 4616*x^5/5! +...
where e.g.f. A(x) satisfies:
A(x) = 1 + x*A(x) + x^2/2!*A(x)^4 + x^3/3!*A(x)^9 + x^4/4!*A(x)^16 +...
Let B(x) = A(x*B(x)) be the e.g.f. of A155807 then:
B(x) = 1 + x*B(x)^2 + x^2/2!*B(x)^6 + x^3/3!*B(x)^12 + x^4/4!*B(x)^20 +...
B(x) = 1 + x + 5*x^2/2! + 55*x^3/3! + 969*x^4/4! + 23661*x^5/5! + 741013*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^2)/k!+x*O(x^n))); n!*polcoeff(A, n)}

Crossrefs

Cf. A155804, A155805, A155807.

Sequence in context: A005264 A195512 A052892 * A196022 A319147 A074706

Adjacent sequences: A155803 A155804 A155805 * A155807 A155808 A155809

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2009

Status

approved