A294040 a(n) = e*(Gamma(2*n,1) - Gamma(n,1)).

0, 1, 14, 321, 13684, 986345, 108504786, 16926795529, 3554627458376, 966858672295089, 330665665961417590, 138879579704199815921, 70273067330329989586044, 42163840398198057552632281, 29599015959535037299068127994, 24034400959142450300350904324985

Offset: 0

Author

Peter Luschny, Nov 14 2017

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..225

Crossrefs

Cf. A000522, A294039.

Programs

Maple

a := n -> exp(1)*(GAMMA(2*n,1) - GAMMA(n,1)):
seq(simplify(a(n)), n=0..15);
# Alternative:
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):
0, seq(A000522(2*n-1)-A000522(n-1),n=1..30); # Robert Israel, Nov 14 2017

Formula

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