A119362 Combinatorial twin prime formulas. This sequence gives the coefficients a(n) of combinatorial sum formulas of n-th twin primes or lesser: twin_prime(n) = 2^(n-6)/(n-1)! Sum_{i=1..n} a(i) * C(n-1,i-1) * (i+2-n).

32, 8, 32, 52, 208, 508, 2672, 9278, 71168, 258772, 2448352, 11401798, 123001112, 660768362, 7257835148, 50721144013, 643561620832, 4610932367548, 57562797069608, 547637465534282, 7281278491404272, 71412114145523938

Offset: 1

Author

André F. Labossière, Jul 24 2006

Keywords

• easy
• nonn

Examples

			twin_prime(10) = [ 2^(10-6)/(10-1)! ] * [ 32*C(10-1,0)*(-7) + 8*C(10-1,1)*(-6) + 32*C(10-1,2)*(-5) + ... + 9278*C(10-1,7)*(0) + 71168*C(10-1,8)*(1) + 258772*C(10-1,9)*(2) ] = 31
		

Crossrefs

Cf. A001097, A000040, A120315, A000166, A115298, A008275.

Programs

Mathematica

Mathematica 5.2 - webMathematica 2 - http://library.wolfram.com/webMathematica/Education/LongDivide.jsp