A294040 - OEIS

%I #7 Nov 15 2017 03:29:17

%S 0,1,14,321,13684,986345,108504786,16926795529,3554627458376,

%T 966858672295089,330665665961417590,138879579704199815921,

%U 70273067330329989586044,42163840398198057552632281,29599015959535037299068127994,24034400959142450300350904324985

%N a(n) = e*(Gamma(2*n,1) - Gamma(n,1)).

%H Robert Israel, <a href="/A294040/b294040.txt">Table of n, a(n) for n = 0..225</a>

%F a(n) = Sum_{k=0..2n-1} (2n-1)!/k! - Sum_{k=0..n-1} (n-1)!/k! = A000522(2*n-1) - A000522(n-1). - _Robert Israel_, Nov 14 2017

%p a := n -> exp(1)*(GAMMA(2*n,1) - GAMMA(n,1)):

%p seq(simplify(a(n)), n=0..15);

%p # Alternative:

%p A000522:= gfun:-rectoproc({(-x-2)*d(1+x)+(x+4)*d(x+2)-d(x+3), d(0) = 1, d(1) = 2, d(2) = 5},d(x),remember):

%p 0, seq(A000522(2*n-1)-A000522(n-1),n=1..30); # _Robert Israel_, Nov 14 2017

%Y Cf. A000522, A294039.

%K nonn

%O 0,3

%A _Peter Luschny_, Nov 14 2017