A233335 E.g.f. A(x) satisfies: A( Integral 1/A(x) dx ) = exp(x).

1, 1, 2, 7, 38, 292, 2975, 38350, 604433, 11351659, 249042701, 6283114723, 179995680530, 5794486077958, 207806806310354, 8241414107222095, 359171801820266717, 17107537203463252273, 886296777786378900077, 49732564234138336160086, 3011177123882906437153214, 196063383282648338166793297

Offset: 0

Author

Paul D. Hanna, Dec 07 2013

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 38*x^4/4! + 292*x^5/5! + 2975*x^6/6! +...
Related expansions.
Integral 1/A(x) dx = x - x^2/2! - x^4/4! - 6*x^5/5! - 52*x^6/6! - 591*x^7/7! - 8404*x^8/8! +...
The series reversion of Integral 1/A(x) dx equals log(A(x)) and begins:
log(A(x)) = x + x^2/2! + 3*x^3/3! + 16*x^4/4! + 126*x^5/5! + 1333*x^6/6! + 17895*x^7/7! + 293461*x^8/8! +...+ A214645(n)*x^n/n! +...
and equals the e.g.f. of A214645.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..160

Crossrefs

Cf. A233336, A214645 (log).

Programs

PARI

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

Formula

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

E.g.f.: exp(G(x)) where G(x) = exp(G(G(x))) is the e.g.f. of A214645.