A174484 - OEIS

%I #2 Mar 30 2012 18:37:21

%S 1,4,45,1041,41629,2582028,230689017,28145738365,4504704373961,

%T 916668654429870,231318743221265869,70928148561381638541,

%U 25983184166531408190165,11210928989636995091435576

%N a(n) = coefficient of x^n/(n-1)! in the (n+2)-th iteration of x*exp(x) for n>=1.

%e The initial n-th iterations of x*exp(x) begin:

%e n=1: x + x^2 + x^3/2! + x^4/3! + x^5/4! + x^6/5! +...

%e n=2: x +2*x^2 + 6*x^3/2! + 23*x^4/3! + 104*x^5/4! + 537*x^6/5! +...

%e n=3: (1)*x +3*x^2 +15*x^3/2! +102*x^4/3! +861*x^5/4! +8598*x^6/5! +...

%e n=4: x +(4)*x^2 +28*x^3/2! +274*x^4/3! +3400*x^5/4! +50734*x^6/5! +...

%e n=5: x + 5*x^2 +(45)*x^3/2! +575*x^4/3! +9425*x^5/4! +187455*x^6/5! +...

%e n=6: x + 6*x^2 +66*x^3/2! +(1041)*x^4/3! +21216*x^5/4!+527631*x^6/5!+...

%e n=7: x + 7*x^2 +91*x^3/2! +1708*x^4/3! +(41629)*x^5/4! +1242892*x^6/5! +...

%e n=8: x + 8*x^2 +120*x^3/2! +2612*x^4/3! +74096*x^5/4!+(2582028)*x^6/5! +...

%e This sequence starts with the above coefficients in parenthesis.

%o (PARI) {a(n)=local(E=x*exp(x+x*O(x^n)), F=x); for(i=1, n+2, F=subst(F, x, E)); (n-1)!*polcoeff(F, n)}

%Y Cf. A174480, A174481, A174482, A174483.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Apr 09 2010