OFFSET
0,3
FORMULA
G.f.: (1-x)^4 / sqrt(1 - 10*x + 33*x^2 - 56*x^3 + 66*x^4 - 54*x^5 + 28*x^6 - 8*x^7 + x^8).
EXAMPLE
G.f.: A(x) = 1 + x + 7*x^2 + 35*x^3 + 171*x^4 + 856*x^5 + 4359*x^6 +...
where
A(x) = 1 + x/(1-x)^5*(1+x) + x^2/(1-x)^10*(1+2^2*x+x^2) + x^3/(1-x)^15*(1+3^2*x+3^2*x^2+x^3) + x^4/(1-x)^20*(1+4^2*x+6^2*x^2+4^2*x^3+x^4) + x^5/(1-x)^25*(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))^(5*m)), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=polcoeff( (1-x)^5 / sqrt(1 - 10*x + 33*x^2 - 56*x^3 + 66*x^4 - 54*x^5 + 28*x^6 - 8*x^7 + x^8 +x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 12 2014
STATUS
approved