A144005 E.g.f. A(x) satisfies: A(x) = 1 + Series_Reversion( Integral A(-x) dx ).

1, 1, 1, 2, 7, 33, 201, 1479, 12842, 127952, 1440989, 18070767, 249766088, 3769280801, 61654447712, 1085974748430, 20485430748783, 411839042136379, 8786499316562396, 198174104269740313, 4708919322491690592

Offset

0,4

Comments

This is essentially the same sequence as A014623. - N. J. A. Sloane, Jul 24 2022

Compare the definition of e.g.f. A(x) to the trivial statement:

if F(x) = 1 + Series_Reversion( Integral F(-x)^2 dx ) then F(x) = 1/(1-x).

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f. satisfies: A(x) = 1 + Integral 1/A(1 - A(x)) dx. - Paul D. Hanna, Jul 10 2015

Example

E.g.f: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 7*x^4/4! + 33*x^5/5! +...
Let I(x) = Series_Reversion(A(x) - 1) = Integral A(-x) dx then
I(x) = x - x^2/2! + x^3/3! - 2*x^4/4! + 7*x^5/5! - 33*x^6/6! +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+serreverse(intformal(subst(A, x, -x)^1))); n!*polcoeff(A, n)}

Crossrefs

Cf. A014623; A144002.

Sequence in context: A059099 A020103 A014623 * A232690 A143889 A350758

Adjacent sequences: A144002 A144003 A144004 * A144006 A144007 A144008

Keyword

nonn

Author

Paul D. Hanna, Sep 07 2008

Status

approved