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A174484 a(n) = coefficient of x^n/(n-1)! in the (n+2)-th iteration of x*exp(x) for n>=1. 5
1, 4, 45, 1041, 41629, 2582028, 230689017, 28145738365, 4504704373961, 916668654429870, 231318743221265869, 70928148561381638541, 25983184166531408190165, 11210928989636995091435576 (list; graph; refs; listen; history; text; internal format)
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: x +2*x^2 + 6*x^3/2! + 23*x^4/3! + 104*x^5/4! + 537*x^6/5! +...

n=3: (1)*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! +...

n=8: x + 8*x^2 +120*x^3/2! +2612*x^4/3! +74096*x^5/4!+(2582028)*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+2, F=subst(F, x, E)); (n-1)!*polcoeff(F, n)}

CROSSREFS

Cf. A174480, A174481, A174482, A174483.

Sequence in context: A197989 A338456 A276292 * A158887 A126452 A082765

Adjacent sequences:  A174481 A174482 A174483 * A174485 A174486 A174487

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 09 2010

STATUS

approved

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Last modified November 26 17:52 EST 2021. Contains 349343 sequences. (Running on oeis4.)