A259822 E.g.f. A(x) satisfies: A( Integral 1/A(x)^3 dx ) = exp(x).

1, 1, 4, 37, 586, 13612, 424621, 16827976, 815866699, 47093387797, 3170897237125, 245127016240321, 21482473673228266, 2112385883734692910, 231062843227493844112, 27913223028923592662539, 3701041353685453743060265, 535729316331363978105167557, 84263588534262286958390813305

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f. satisfies: A(x) = exp( Series_Reversion( Integral 1/A(x)^3 dx ) ).

E.g.f. A(x) such that A(x/3)^3 is the e.g.f. of A233335.

Example

E.g.f.: A(x) = 1 + x + 4*x^2/2! + 37*x^3/3! + 586*x^4/4! + 13612*x^5/5! + 424621*x^6/6! +...
where log(A(x)) = Series_Reversion( Integral 1/A(x)^3 dx ):
log(A(x)) = x + 3*x^2/2! + 27*x^3/3! + 432*x^4/4! + 10206*x^5/5! + 323919*x^6/6! +...+ 3^(n-1)*A214645(n)*x^n/n! +...
and
A(x/3)^3 = 1 + x + 2*x^2/2! + 7*x^3/3! + 38*x^4/4! + 292*x^5/5! + 2975*x^6/6! +...+ A233335(n)*x^n/n! +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(serreverse(intformal(1/A^3+x*O(x^n))))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A233335, A214645.

Sequence in context: A001518 A185082 A377741 * A345102 A036245 A133471

Adjacent sequences: A259819 A259820 A259821 * A259823 A259824 A259825

Keyword

nonn

Author

Paul D. Hanna, Jul 05 2015

Status

approved