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

1,2

Links

Table of n, a(n) for n=1..17.

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.

Example

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

Prog

(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))))}

Crossrefs

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

Sequence in context: A302583 A302605 A303260 * A128318 A032274 A374601

Adjacent sequences: A174491 A174492 A174493 * A174495 A174496 A174497

Keyword

nonn

Author

Paul D. Hanna, Apr 17 2010

Status

approved