OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} binomial(prime(k), n-k).
EXAMPLE
G.f.: A(x) = x + 3*x^2 + 5*x^3 + 9*x^4 + 19*x^5 + 43*x^6 + 109*x^7 + 297*x^8 +...
where
A(x) = x*(1+x)^2 + x^2*(1+x)^3 + x^3*(1+x)^5 + x^4*(1+x)^7 + x^5*(1+x)^11 + x^6*(1+x)^13 + x^7*(1+x)^17 + x^8*(1+x)^19 +...+ x^n*(1+x)^prime(n) +...
PROG
(PARI) {a(n)=polcoeff(sum(m=1, n, x^m*(1+x+x*O(x^n))^prime(m)), n)}
for(n=1, 40, print1(a(n), ", "))
(PARI) {a(n) = sum(k=1, n, binomial(prime(k), n-k))}
for(n=1, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 14 2013
STATUS
approved