A155804 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n-1)/2).

1, 1, 1, 4, 19, 161, 1606, 21022, 323485, 5874913, 122077756, 2871573596, 75437801539, 2193468714373, 70020045331510, 2437979768144026, 92073099488632441, 3753886179551636513, 164556499026975482008

Offset: 0

Author

Paul D. Hanna, Jan 27 2009

Keywords

• nonn

Examples

			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! +...
		

Crossrefs

Cf. A155805, A155806, A155807, A107590, A219358.

Programs

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)}

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.