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A209276 O.g.f. satisfies: A(x) = Sum_{n>=0} (n+2)^n * x^n * A((n+2)*x)^n/n! * exp(-(n+2)*x*A((n+2)*x)). 3
1, 1, 6, 133, 9403, 2065969, 1400088539, 2908156231705, 18410003437367130, 353588715425938097698, 20534146782689861283550052, 3596867485365965032072729708845, 1897112888731795684931545113460297299, 3009299517165127420220975531888408947667944 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to the LambertW identity:

Sum_{n>=0} (n+2)^n * x^n * G(x)^n/n! * exp(-(n+2)*x*G(x)) = 1/(1 - x*G(x)).

LINKS

Table of n, a(n) for n=0..13.

EXAMPLE

O.g.f.: A(x) = 1 + x + 6*x^2 + 133*x^3 + 9403*x^4 + 2065969*x^5 +...

where

A(x) = exp(-2*x*A(2*x)) + 3*x*A(3*x)*exp(-3*x*A(3*x)) + 4^2*x^2*A(4*x)^2/2!*exp(-4*x*A(4*x)) + 5^3*x^3*A(5*x)^3/3!*exp(-5*x*A(5*x)) + 6^4*x^4*A(6*x)^4/4!*exp(-6*x*A(6*x)) + 7^5*x^5*A(7*x)^5/5!*exp(-7*x*A(7*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+2)^k*x^k*subst(A, x, (k+2)*x)^k/k!*exp(-(k+2)*x*subst(A, x, (k+2)*x)+x*O(x^n)))); polcoeff(A, n)}

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

CROSSREFS

Cf. A218672, A193363, A209277.

Sequence in context: A247012 A003373 A129047 * A244745 A179564 A263583

Adjacent sequences:  A209273 A209274 A209275 * A209277 A209278 A209279

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 15 2013

STATUS

approved

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Last modified March 8 07:17 EST 2021. Contains 341941 sequences. (Running on oeis4.)