A103732 Negative of column k=5 sequence of array A103728.

5, 229, 731, 4111, 8117, 25189, 94891, 137909, 366803, 641959, 830885, 1341589, 2549923, 4504453, 5371979, 8803541, 11932549, 13799879, 20843861, 26956597, 38735575, 60493919, 74542099, 82483013, 100393765, 110446523, 132966511

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. A000040, A103718, A103728.

Formula

a(n) = -A103728(n+4, 5)=-(1 -(p(n+4)-1)*binomial(p(n+4)-1, 5))/p(n+4), with p(n):=A000040(n) (n-th prime).

a(n) = -(394 - 499*p(n+4) + 310*p(n+4)^2 - 100*p(n+4)^3 + 16*p(n+4)^4 - p(n+4)^5)/5! = -(Sum_{m=0..5} A103718(k, m)*p(n+4)^m)/5!.