A247331 G.f. satisfies: A(x) = Sum_{n>=0} x^n * (3 + A(x)^n)^n.

1, 4, 20, 148, 1492, 18068, 244628, 3582612, 55783252, 913716116, 15633525524, 278068128660, 5124595687636, 97633146977428, 1919960496128660, 38930551809036436, 813367272118600276, 17501331733030883732, 387693438148021391892, 8839040069648710445460

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2)/(1 - 3*x*A(x)^n)^(n+1).

Example

 G.f.: A(x) = 1 + 4*x + 20*x^2 + 148*x^3 + 1492*x^4 + 18068*x^5 +...
where the g.f. satisfies following series identity:
A(x) = 1 + x*(3+A(x)) + x^2*(3+A(x)^2)^2 + x^3*(3+A(x)^3)^3 + x^4*(3+A(x)^4)^4 + x^5*(3+A(x)^5)^5 + x^6*(3+A(x)^6)^6 +...
A(x) = 1/(1-3*x) + x*A(x)/(1-3*x*A(x))^2 + x^2*A(x)^4/(1-3*x*A(x)^2)^3 + x^3*A(x)^9/(1-3*x*A(x)^3)^4 + x^4*A(x)^16/(1-3*x*A(x)^4)^5 + x^5*A(x)^25/(1-3*x*A(x)^5)^6 + x^6*A(x)^36/(1-3*x*A(x)^6)^7 +...

Prog

 (PARI) {a(n, t=3)=local(A=1+x); for(i=1, n, A=sum(k=0, n, A^(k^2)*x^k/(1 - t*A^k*x +x*O(x^n))^(k+1) )); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n, t=3)=local(A=1+x); for(i=1, n, A=sum(k=0, n, x^k * (t + A^k +x*O(x^n))^k)); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A247330, A203000.

Sequence in context: A117887 A082988 A001171 * A167018 A094070 A335627

Adjacent sequences: A247328 A247329 A247330 * A247332 A247333 A247334

Keyword

nonn

Author

Paul D. Hanna, Sep 14 2014

Status

approved