A103730 - OEIS

%I #4 Jun 16 2016 23:27:27

%S 3,17,109,203,527,773,1473,3163,3929,6947,9639,11213,14857,21683,

%T 30333,33659,45077,53969,58823,75113,87493,108503,141407,160099,

%U 170033,191117,202283,225903,322937,355029,407047,425453,525843,547649,616667,691253

%N Negative of column k=3 sequence of array A103728.

%C The two a(n) formulas, given below, produce natural numbers for all n>=0.

%F a(n)=-A103728(n+3, 3)=-(1 -(p(n+3)-1)*binomial(p(n+3)-1, 3))/p(n+3), with p(n):=A000040(n) (n-th prime).

%F a(n)= -(17 - 17*p(n+3) + 7*p(n+3)^2 - p(n+3)^3)/3! = -sum(A103718(k, m)*p(n+3)^m, m=0..3)/3!.

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Feb 24 2005