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

1,3

Comments

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

Links

Paul D. Hanna, Table of n, a(n) for n = 1..105

Example

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 parenthesis.

Prog

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

Crossrefs

Cf. A174480, A174482, A174483, A174484.

Sequence in context: A382950 A022025 A302911 * A306205 A106303 A157518

Adjacent sequences: A174478 A174479 A174480 * A174482 A174483 A174484

Keyword

nonn

Author

Paul D. Hanna, Apr 09 2010

Status

approved