A218676 O.g.f. satisfies: A(x) = Sum_{n>=0} n^n * x^n*A(n*x)^(5*n)/n! * exp(-n*x*A(n*x)^5).

1, 1, 6, 71, 1311, 34146, 1207717, 57298282, 3653975784, 316252925221, 37596625187796, 6206102367103899, 1434418185304457039, 466995106832397752352, 215051811411620578152401, 140491107719613466192347681, 130481943378389095603359529403

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..16.

Example

O.g.f.: A(x) = 1 + x + 6*x^2 + 71*x^3 + 1311*x^4 + 34146*x^5 + 1207717*x^6 +...
where
A(x) = 1 + x*A(x)^5*exp(-x*A(x)^5) + 2^2*x^2*A(2*x)^10/2!*exp(-2*x*A(2*x)^5) + 3^3*x^3*A(3*x)^15/3!*exp(-3*x*A(3*x)^5) + 4^4*x^4*A(4*x)^20/4!*exp(-4*x*A(4*x)^5) + 5^5*x^5*A(5*x)^25/5!*exp(-5*x*A(5*x)^5) +...
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^5, x, k*x)^k/k!*exp(-k*x*subst(A^5, x, k*x)+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A218672, A218673, A218674, A218675.

Cf. A217900, A218670, A218667, A218668, A218669, A134055.

Sequence in context: A349684 A349598 A145089 * A127135 A187651 A357141

Adjacent sequences: A218673 A218674 A218675 * A218677 A218678 A218679

Keyword

nonn

Author

Paul D. Hanna, Nov 04 2012

Status

approved