A174493 a(n) = coefficient of x^n/(n-1)! in the 3-fold iteration of x*exp(x).

1, 3, 15, 102, 861, 8598, 98547, 1270160, 18138601, 283754826, 4818884319, 88186786020, 1728395865021, 36091833338174, 799408841413051, 18708996086926272, 461095012437724881, 11931573394008790290

Offset: 1

Author

Paul D. Hanna, Apr 17 2010

Keywords

• nonn

Examples

			E.g.f.: x + 3*x^2 + 15*x^3/2! + 102*x^4/3! + 861*x^5/4! +...
		

Crossrefs

Cf. A174480, A080108, A174494, A174495, A174496.

Programs

PARI

{a(n)=local(F=x, xEx=x*exp(x+x*O(x^n)));for(i=1,3,F=subst(F, x, xEx));(n-1)!*polcoeff(F, n)}

PARI

{a(n)=sum(k=0,n-1,binomial(n-1,k)*sum(j=0,n-1-k,binomial(n-1-k,j)*(k+1)^j*(k+1+j)^(n-1-k-j)))}

Formula

a(n) = Sum_{k=0..n, j=0..n-k} C(n,k)*C(n-k,j)*(k+1)^j*(k+1+j)^(n-k-j).

O.g.f.: Sum_{n>=1} A080108(n)*x^n/(1-n*x)^n, where A080108(n) = [x^n/(n-1)! ] E(E(x)) and E(x) = x*exp(x).