OFFSET
0,3
FORMULA
G.f.: (1-x)^5 / sqrt((1 - 3*x + x^2)*(1 - x + 2*x^2 - x^3)*(1 - 8*x + 14*x^2 - 12*x^3 + 5*x^4 - x^5)).
G.f.: (1-x)^5 / sqrt(1 - 12*x + 52*x^2 - 124*x^3 + 206*x^4 - 246*x^5 + 208*x^6 - 120*x^7 + 45*x^8 - 10*x^9 + x^10).
EXAMPLE
G.f.: A(x) = 1 + x + 8*x^2 + 44*x^3 + 232*x^4 + 1253*x^5 + 6895*x^6 +...
where
A(x) = 1 + x/(1-x)^6*(1+x) + x^2/(1-x)^12*(1+2^2*x+x^2) + x^3/(1-x)^18*(1+3^2*x+3^2*x^2+x^3) + x^4/(1-x)^24*(1+4^2*x+6^2*x^2+4^2*x^3+x^4) + x^5/(1-x)^30*(1+5^2*x+10^2*x^2+10^2*x^3+5^2*x^4+x^5) +...
PROG
(PARI) {a(n)=polcoeff( sum(m=0, n, x^m * sum(k=0, m, binomial(m, k)^2 * x^k) / (1-x +x*O(x^n))^(6*m)), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=polcoeff( (1-x)^5 / sqrt((1 - 3*x + x^2)*(1 - x + 2*x^2 - x^3)*(1 - 8*x + 14*x^2 - 12*x^3 + 5*x^4 - x^5) +x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 12 2014
STATUS
approved