A174482 a(n) = coefficient of x^n/(n-1)! in the n-th iteration of x*exp(x) for n>=1.

1, 2, 15, 274, 9425, 527631, 43806175, 5060694920, 776717906529, 152926864265845, 37581193509020711, 11276280009364700628, 4057223684795928824281, 1724304353051995724792979

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Example

The initial n-th iterations of x*exp(x) begin:
n=1: (1)*x + x^2 + x^3/2! + x^4/3! + x^5/4! + x^6/5! +...
n=2: x +(2)*x^2 + 6*x^3/2! + 23*x^4/3! + 104*x^5/4! + 537*x^6/5! +...
n=3: x + 3*x^2 +(15)*x^3/2! +102*x^4/3! +861*x^5/4! +8598*x^6/5! +...
n=4: x + 4*x^2 +28*x^3/2! +(274)*x^4/3! +3400*x^5/4! +50734*x^6/5! +...
n=5: x + 5*x^2 +45*x^3/2! +575*x^4/3! +(9425)*x^5/4! +187455*x^6/5! +...
n=6: x + 6*x^2 +66*x^3/2! +1041*x^4/3! +21216*x^5/4!+(527631)*x^6/5!+...
This sequence starts with the above coefficients in parathesis.

Prog

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

Crossrefs

Cf. A174480, A174481, A174483, A174484.

Sequence in context: A192567 A354980 A143886 * A076111 A371673 A087526

Adjacent sequences: A174479 A174480 A174481 * A174483 A174484 A174485

Keyword

nonn

Author

Paul D. Hanna, Apr 09 2010

Status

approved