login
A103730
Negative of column k=3 sequence of array A103728.
0
3, 17, 109, 203, 527, 773, 1473, 3163, 3929, 6947, 9639, 11213, 14857, 21683, 30333, 33659, 45077, 53969, 58823, 75113, 87493, 108503, 141407, 160099, 170033, 191117, 202283, 225903, 322937, 355029, 407047, 425453, 525843, 547649, 616667, 691253
OFFSET
0,1
COMMENTS
The two a(n) formulas, given below, produce natural numbers for all n>=0.
FORMULA
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).
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!.
CROSSREFS
Sequence in context: A299039 A123772 A212524 * A074556 A295808 A215048
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 24 2005
STATUS
approved