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

0,1

Comments

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

Links

Table of n, a(n) for n=0..20.

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!.

Crossrefs

Sequence in context: A061643 A209842 A211154 * A177491 A269087 A166843

Adjacent sequences: A103732 A103733 A103734 * A103736 A103737 A103738

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 24 2005

Status

approved