A120315 Combinatorial prime formulas. This sequence gives the coefficients a(n) of combinatorial sum formulas of n-th primes or lesser: prime(n) = 2^(n-5)/(n-1)! Sum_{i=1..n} a(i) * C(n-1,i-1) * (1-(n-i)/2).

32, 8, 32, 52, 208, 508, 2672, 9278, 56048, 304132, 1654552, 12649198, 79342112, 615363002, 5010269828, 43213043413, 393086195632, 3633203615548, 38586294965048, 389261740224662, 4344329090764472, 51205748753742838

Offset: 1

Author

André F. Labossière, Jun 20 2006

Keywords

• easy
• nonn

Examples

			prime(7) = [ 2^(7-5)/(7-1)! ] * [ 32*C(7-1,0)*(1-(7-1)/2) + 8*C(7-1,1)*(1-(7-2)/2) + 32*C(7-1,2)*(1-(7-3)/2) + 52*C(7-1,3)*(1-(7-4)/2) + 208*C(7-1,4)*(1-(7-5)/2) + 508*C(7-1,5)*(1-(7-6)/2) + 2672*C(7-1,6)*(1-(7-7)/2) ] = 17
		

Crossrefs

Cf. A000040, A007504, A000166, A115298, A008275.