A177779 E.g.f.: A(x) = Sum_{n>=0} (1/n!)*Product_{k=0..n-1} L(3^k*x), where L(x) is the e.g.f. of A177780.

1, 1, 7, 159, 10065, 1769889, 892392183, 1321983917631, 5822841033057825, 76645599313018616001, 3021493143896197748386407, 357064253282406274455859700319, 126544129732367263008235662373092465

Offset: 0

Author

Paul D. Hanna, May 20 2010

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 7*x^2/2! + 159*x^3/3! + 10065*x^4/4! +...
Then e.g.f. A(x) is given by:
A(x) = 1 + L(x) + L(x)L(3x)/2! + L(x)L(3x)L(9x)/3! + L(x)L(3x)L(9x)L(27x)/4! +...
where L(x) is the e.g.f. of A177780:
. L(x) = x + 4*x^2/2! + 60*x^3/3! + 2496*x^4/4! + 276240*x^5/5! +...
. L(x) = x*d/dx log( Sum_{n>=0} 3^(n(n-1)/2)*x^n/n! )
and satisfies:
. L(x)/x = 1 + 2*L(x) + 2^2*L(x)L(3x)/2! + 2^3*L(x)L(3x)L(9x)/3! + 2^4*L(x)L(3x)L(9x)L(27x)/4! +...
		

Crossrefs

Cf. A177780.

Programs

PARI

{a(n,q=3)=local(Lq=x+x^2,A); for(i=1,n,Lq=x*sum(m=0,n,(q-1)^m/m!*prod(k=0,m-1,subst(Lq,x,q^k*x+x*O(x^n))))); A=sum(m=0,n,1/m!*prod(k=0,m-1,subst(Lq,x,q^k*x+x*O(x^n))));n!*polcoeff(A,n)}