A103735 Column k=8 sequence of array A103728.

41, 457, 12113, 41455, 305867, 3000929, 5664121, 29442493, 75028961, 115285297, 255381053, 738339317, 1884309221, 2516676241, 5657847163, 9307388231, 11805057217, 23150085349, 35212054847, 63554702993, 131233995553

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, 8)=(1 +(p(n+5)-1)*binomial(p(n+5)-1, 8))/p(n+5), with p(n):=A000040(n) (n-th prime).

a(n)= (149904 - 227708*p(n+5) + 185408* p(n+5)^2 - 89733*p(n+5)^3 + 26985*p(n+5)^4 - 5082*p(n+5)^5 + 582*p(n+5)^6 - 37*p(n+5)^7 + 1*p(n+5)^8)/8! = sum(A103718(k, m)*p(n+5)^m, m=0..8)/8!.