A144003 - OEIS

%I #8 Sep 07 2024 16:37:00

%S 1,1,3,24,339,7101,200961,7256277,321662502,17029233774,1054682936433,

%T 75199620036177,6094256204678922,555527437385512095,

%U 56468189426338157580,6353824422205136494044,786458781488123265873519

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

%H Paul D. Hanna, <a href="/A144003/b144003.txt">Table of n, a(n) for n = 0..201</a>

%F E.g.f. A(x) satisfies: A'(x) = A(A(x) - 1)^3. - _Paul D. Hanna_, Aug 26 2024

%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 24*x^3/3! + 339*x^4/4! + 7101*x^5/5! + 200961*x^6/6! + 7256277*x^7/7! + 321662502*x^8/8! + ...

%e where A(x) = 1 + Series_Reversion( Integral 1/A(x)^3 dx ).

%e RELATED SERIES.

%e Integral 1/A(x)^3 dx = x - 3*x^2/2! + 3*x^3/3! - 24*x^4/4! - 261*x^5/5! - 6543*x^6/6! - 202671*x^7/7! - 7911351*x^8/8! + ...

%e where Integral 1/A(x)^3 dx = Series_Reversion(A(x) - 1).

%e A(A(x) - 1) = 1 + x + 6*x^2/2! + 75*x^3/3! + 1479*x^4/4! + 40617*x^5/5! + 1447785*x^6/6! + 64027656*x^7/7! + 3404869020*x^8/8! + ...

%e A(A(x) - 1)^3 = 1 + 3*x + 24*x^2/2! + 339*x^3/3! + 7101*x^4/4! + ...

%e where A(A(x) - 1)^3 = d/dx A(x).

%o (PARI) {a(n) = my(A=1+x+x*O(x^n)); for(i=0,n, A = 1 + serreverse(intformal(1/A^3))); n!*polcoeff(A,n)}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A001028, A144002, A144004.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 07 2008