A203000 G.f. satisfies: A(x) = Sum_{n>=0} x^n * (A(x)^n + 1)^n.

1, 2, 6, 30, 198, 1526, 13014, 119454, 1161094, 11828966, 125456438, 1378837422, 15654724742, 183216332886, 2207257195798, 27347515306814, 348276224255878, 4557686850206662, 61280403794571894, 846507901281129550, 12013072624622078854, 175127895948991871542

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..150

Formula

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

Example

G.f.: A(x) = 1 + 2*x + 6*x^2 + 30*x^3 + 198*x^4 + 1526*x^5 + 13014*x^6 +...
where the g.f. satisfies following series identity:
A(x) = 1 + (A(x)+1)*x + (A(x)^2+1)^2*x^2 + (A(x)^3+1)^3*x^3 + (A(x)^4+1)^4*x^4 +...
A(x) = 1/(1-x) + x*A(x)/(1-x*A(x))^2 + x^2*A(x)^4/(1-x*A(x)^2)^3 + x^3*A(x)^9/(1-x*A(x)^3)^4 + x^4*A(x)^16/(1-x*A(x)^4)^5 +...

Prog

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

Crossrefs

Cf. A247330, A203014, A186998, A186999.

Sequence in context: A340243 A078700 A176719 * A334317 A104561 A211211

Adjacent sequences: A202997 A202998 A202999 * A203001 A203002 A203003

Keyword

nonn

Author

Paul D. Hanna, Dec 27 2011

Status

approved