A119362 - OEIS

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).

%I #8 Jun 16 2016 23:27:30

%S 32,8,32,52,208,508,2672,9278,71168,258772,2448352,11401798,123001112,

%T 660768362,7257835148,50721144013,643561620832,4610932367548,

%U 57562797069608,547637465534282,7281278491404272,71412114145523938

%N 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).

%e 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

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

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

%K easy,nonn

%O 1,1

%A _André F. Labossière_, Jul 24 2006