A193160 E.g.f. A(x) satisfies: A(x/(1-x)) = x*A'(x).

1, 2, 9, 68, 760, 11664, 233828, 5905696, 182846592, 6792372480, 297550188672, 15153482847744, 886517886778368, 58975120009537536, 4422337095720648960, 370957479138591903744, 34576037926690499493888, 3559813114275891217760256

Offset: 1

Author

Paul D. Hanna, Jul 16 2011

Keywords

• nonn

Examples

			E.g.f.: A(x) = x + 2*x^2/2! + 9*x^3/3! + 68*x^4/4! + 760*x^5/5! +...
Related expansions:
A(x/(1-x)) = x + 4*x^2/2! + 27*x^3/3! + 272*x^4/4! + 3800*x^5/5! +...
x*A'(x) = x + 4*x^2/2! + 27*x^3/3! + 272*x^4/4! + 3800*x^5/5! +...
		

Crossrefs

Cf. A193161, A001063.

Programs

PARI

{a(n)=local(A=[1],F=x);for(i=1,n,A=concat(A,0);F=x*Ser(A);A[#A]=Vec(subst(F,x,x/(1-x)))[#A]/(#A-1));if(n<1,0,n!*A[n])}

PARI

{a(n)=if(n<1,0,if(n==1,1,n!/(n-1)*sum(k=1,n-1,binomial(n-1,k-1)*a(k)/k!)))}

Formula

a(n) = n*(n-2)!* Sum_{k=1..n-1} C(n-1,k-1)* a(k)/k! for n>1 with a(1)=1.

a(n) = n*A193161(n-1).