A103914 Negative of column k=9 sequence of array A103728.

9, 203, 10767, 46061, 475793, 6668731, 13845629, 91598867, 266769639, 435522233, 1078275557, 3609658883, 10468384561, 14540796059, 36461681717, 64117563369, 83947073543, 180056219381, 289521339853, 564930693271, 1283176845407

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.

Crossrefs

Cf. A103735 (k=8).

Formula

a(n)=-A103728(n+5, 9)=-(1 -(p(n+5)-1)*binomial(p(n+5)-1, 9))/p(n+5), with p(n):=A000040(n) (n-th prime).

a(n)= -(1389456 - 2199276*p(n+5) + 1896380*p(n+5)^2 - 993005*p(n+5)^3 + 332598*p(n+5)^4 - 72723*p(n+5)^5 + 10320*p(n+5)^6 - 915*p(n+5)^7 + 46*p(n+5)^8 - p(n+5)^9)/9! = -sum(A103718(k, m)*p(n+5)^m, m=0..9)/9!.