A174481 a(n) = coefficient of x^n/(n-1)! in the (n-1)-th iteration of x*exp(x) for n>=1.

1, 1, 6, 102, 3400, 187455, 15441636, 1776667928, 272145104736, 53540399628405, 13156413372354340, 3949011172491569316, 1421739781364268435576, 604701975767931070422939, 299969585267917154906689660

Offset: 1

Author

Paul D. Hanna, Apr 09 2010

Keywords

• nonn

Examples

			The initial n-th iterations of x*exp(x) begin:
n=0: (1)*x;
n=1: x + (1)*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! + (15441636)*x^7/6! +...
This sequence starts with the above coefficients in parathesis.
		

Crossrefs

Cf. A174480, A174482, A174483, A174484.

Programs

PARI

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