A174483 a(n) = coefficient of x^n/(n-1)! in the (n+1)-th iteration of x*exp(x) for n>=1.

1, 3, 28, 575, 21216, 1242892, 106459312, 12577403841, 1962856001440, 391431498879806, 97160350830990624, 29387077319612739025, 10642369538735639329912, 4547196797035053394680280

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: x + x^2 + x^3/2! + x^4/3! + x^5/4! + x^6/5! +...
n=2: (1)*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!+...
n=7: x + 7*x^2 +91*x^3/2! +1708*x^4/3! +41629*x^5/4! +(1242892)*x^6/5! +...
This sequence starts with the above coefficients in parenthesis.

Prog

(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)}

Crossrefs

Cf. A174480, A174481, A174482, A174484.

Sequence in context: A062497 A367391 A056066 * A092985 A331196 A181588

Adjacent sequences: A174480 A174481 A174482 * A174484 A174485 A174486

Keyword

nonn

Author

Paul D. Hanna, Apr 09 2010

Status

approved