OFFSET
0,3
COMMENTS
FORMULA
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 22*x^3 + 141*x^4 + 986*x^5 + 7295*x^6 +...
The g.f. satisfies:
F(x) = 1 + x*A(x)^3 + x^2*A(x)^6 + x^3*A(x)^10 + x^4*A(x)^13 + x^5*A(x)^17 + x^6*A(x)^20 + x^7*A(x)^23 +...+ x^n*A(x)^A001952(n) +...
The g.f. of A190270, F(x) = A(x/F(x)^2), satisfies:
F(x) = 1 + x*F(x) + x^2*F(x)^2 + x^3*F(x)^4 + x^4*F(x)^5 + x^5*F(x)^7 + x^6*F(x)^8 + x^7*F(x)^9 + x^8*F(x)^11 +...+ x^n*F(x)^A001951(n) +...
and begins:
F(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 49*x^5 + 169*x^6 + 605*x^7 +...
Since A(x) = F(x*A(x)^2), then:
A(x) = 1 + x*A(x)^2 + 2*x^2*A(x)^4 + 5*x^3*A(x)^6 + 15*x^4*A(x)^8 +...
PROG
(PARI) {a(n)=local(A=1+x, t=sqrt(2)-1); for(i=1, n, A=sum(m=0, n, x^m*(A+x*O(x^n))^floor(m+m/t))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 06 2011
STATUS
approved