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%I #5 Jul 14 2013 12:11:16
%S 1,3,7,16,38,96,262,767,2346,7315,22954,72239,228484,730470,2379669,
%T 7960733,27453387,97418566,353442491,1300699953,4821108695,
%U 17903653177,66375491706,245111697148,900578294735,3292301955863,11991348060873,43624020578230,159059383244035,583396507916927
%N G.f.: Sum_{n>=1} x^n / (1-x)^prime(n).
%F a(n) = Sum_{k=1..n} binomial(prime(k) + n-k-1, n-k).
%e G.f.: A(x) = x + 3*x^2 + 7*x^3 + 16*x^4 + 38*x^5 + 96*x^6 + 262*x^7 + 767*x^8 +...
%e where
%e 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) +...
%o (PARI) {a(n)=polcoeff(sum(m=1, n, x^m/(1-x+x*O(x^n))^prime(m)), n)}
%o for(n=1, 40, print1(a(n), ", "))
%o (PARI) {a(n) = sum(k=1, n, binomial(prime(k)+n-k-1, n-k))}
%o for(n=1, 40, print1(a(n), ", "))
%Y Cf. A227234, A000040.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jul 14 2013
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