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A218681 O.g.f. satisfies: A(x) = Sum_{n>=0} n^n * x^n * A(n^2*x)^n/n! * exp(-n*x*A(n^2*x)). 8
1, 1, 2, 17, 248, 8044, 499033, 62625238, 15947986557, 8220983161264, 8675909809528468, 18709697284980554577, 82551047593942653184220, 747564468621251440782891798, 13885138852461763218258064204207, 529723356811556257370919794910913765 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to the LambertW identity:

Sum_{n>=0} n^n * x^n * G(x)^n/n! * exp(-n*x*G(x)) = 1/(1 - x*G(x)).

LINKS

Table of n, a(n) for n=0..15.

EXAMPLE

O.g.f.: A(x) = 1 + x + 2*x^2 + 17*x^3 + 248*x^4 + 8044*x^5 + 499033*x^6 +...

where

A(x) = 1 + x*A(x)*exp(-x*A(x)) + 2^2*x^2*A(2^2*x)^2/2!*exp(-2*x*A(2^2*x)) + 3^3*x^3*A(3^2*x)^3/3!*exp(-3*x*A(3^2*x)) + 4^4*x^4*A(4^2*x)^4/4!*exp(-4*x*A(4^2*x)) + 5^5*x^5*A(5^2*x)^5/5!*exp(-5*x*A(5^2*x)) +...

simplifies to a power series in x with integer coefficients.

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, k^k*x^k*subst(A, x, k^2*x)^k/k!*exp(-k*x*subst(A, x, k^2*x)+x*O(x^n)))); polcoeff(A, n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A218672, A219342, A185029.

Sequence in context: A342205 A099694 A099698 * A098622 A020561 A099702

Adjacent sequences:  A218678 A218679 A218680 * A218682 A218683 A218684

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 06 2012

STATUS

approved

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Last modified August 4 16:10 EDT 2021. Contains 346447 sequences. (Running on oeis4.)