A174484 a(n) = coefficient of x^n/(n-1)! in the (n+2)-th iteration of x*exp(x) for n>=1.

1, 4, 45, 1041, 41629, 2582028, 230689017, 28145738365, 4504704373961, 916668654429870, 231318743221265869, 70928148561381638541, 25983184166531408190165, 11210928989636995091435576

Offset

1,2

Comments

Compare to [x^n] x/(1-(n+2)*x) = (n+2)^(n-1) where x/(1-(n+2)*x) is the (n+2)-th iteration of x/(1-x). - Paul D. Hanna, Apr 06 2026

Links

Paul D. Hanna, Table of n, a(n) for n = 1..100

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) = my(E=x*exp(x+x*O(x^n)), F=x); for(i=1, n+2, F=subst(F, x, E)); (n-1)!*polcoef(F, n)}

Crossrefs

Cf. A174480, A174481, A174482, A174483.

Sequence in context: A380829 A338456 A276292 * A158887 A126452 A082765

Adjacent sequences: A174481 A174482 A174483 * A174485 A174486 A174487

Keyword

nonn

Author

Paul D. Hanna, Apr 09 2010

Status

approved