A103734 Negative of column k=7 sequence of array A103728.

109, 731, 10767, 30149, 163129, 1143211, 1970129, 8122067, 18188839, 26350925, 52385857, 131260323, 295577917, 379875659, 767165717, 1181890569, 1452930119, 2608460321, 3755952517, 6277007703, 11796314207, 15849070099, 18287662313

Offset: 0

Author

Wolfdieter Lang, Feb 24 2005

Keywords

• nonn
• easy

Comments

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

Formula

a(n)=-A103728(n+5, 7)=-(1 -(p(n+5)-1)*binomial(p(n+5)-1, 7))/p(n+5), with p(n):=A000040(n) (n-th prime).

a(n)= -(18108 - 26200*p(n+5) + 19901*p(n+5)^2 - 8729*p(n+5)^3 + 2282*p(n+5)^4 - 350*p(n+5)^5 + 29*p(n+5)^6 - p(n+5)^7)/7! = -sum(A103718(k, m)*p(n+5)^m, m=0..7)/7!.