A174494 a(n) = coefficient of x^n/(n-1)! in the 4-fold iteration of x*exp(x).

1, 4, 28, 274, 3400, 50734, 880312, 17357736, 382463824, 9298086490, 246914949376, 7104423326356, 220000621675912, 7290852811359654, 257332393857067720, 9632914084301343304, 381050245422453157408

Offset: 1

Author

Paul D. Hanna, Apr 17 2010

Keywords

• nonn

Examples

			E.g.f.: x + 4*x^2 + 28*x^3/2! + 274*x^4/3! + 3400*x^5/4! +...
		

Crossrefs

Cf. A174480, A080108, A174493, A174495, A174496.

Programs

PARI

{a(n)=local(F=x, xEx=x*exp(x+x*O(x^n)));for(i=1,4,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*sum(i=0,n-1-k-j,binomial(n-1-k-j,i)*(k+1+j)^i*(k+1+j+i)^(n-1-k-j-i))))}

Formula

O.g.f.: Sum_{n>=1} A174493(n)*x^n/(1-n*x)^n, where A174493(n) = [x^n/(n-1)! ] E(E(E(x))) and E(x) = x*exp(x).

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

E.g.f. equals the 2-fold iteration of the e.g.f. of A080108.