OFFSET
1,2
FORMULA
EXAMPLE
G.f.: C(x) = x + 5*x^2 + 25*x^3 + 215*x^4 + 1825*x^5 + 17525*x^6 +...
Related series:
A(x) = x + 2*x^2 + 16*x^3 + 122*x^4 + 1096*x^5 + 10322*x^6 +...
B(x) = x + 3*x^2 + 21*x^3 + 153*x^4 + 1401*x^5 + 13083*x^6 +...
where C(x) = x + 5*A(x)*B(x).
(C(x)^2 - x*C(x))/5 = x^3 + 10*x^4 + 93*x^5 + 920*x^6 + 9305*x^7 + 97050*x^8 + 1031737*x^9 +...
PROG
(PARI) {a(n)=local(A=x+x^2, B=x+2*x^2, C=x+3*x^2); for(i=1, n, A=x+2*B*C+x*O(x^n); B=x+3*A*C+x*O(x^n); C=x+5*A*B+x*O(x^n)); polcoeff(C, n)}
for(n=1, 30, print1(a(n), ", "))
(PARI) {a(n)=local(C=x); for(i=1, n, C=x+5*x^2*(1+2*C)*(1+3*C)/(1-6*C^2 +x*O(x^n))^2); polcoeff(C, n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 30 2013
STATUS
approved