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A227235 G.f.: Sum_{n>=1} x^n / (1-x)^prime(n). 1

%I

%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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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)