A294039 a(n) = e*Gamma(2*n,1).

2, 16, 326, 13700, 986410, 108505112, 16926797486, 3554627472076, 966858672404690, 330665665962404000, 138879579704209680022, 70273067330330098091156, 42163840398198058854693626, 29599015959535037315994925480, 24034400959142450300587879489790

Offset: 1

Author

Peter Luschny, Nov 14 2017

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..225

Crossrefs

Bisection of A000522. Cf. A294040.

Programs

Maple

a := n -> exp(1)*GAMMA(2*n,1):
seq(simplify(a(n)), n=1..15);
# Alternate:
f:= gfun:-rectoproc({a(n+1) = 2*n*(2*n+1)*a(n) + 2*n+2, a(1) = 2},a(n),remember):
map(f, [$1..20]); # Robert Israel, Nov 14 2017

Mathematica

Array[E Gamma[2 #, 1] &, 15] (* Michael De Vlieger, Nov 14 2017 *)

Formula

From Robert Israel, Nov 14 2017: (Start)

a(n) = (2*n-1)!*Sum_{k=0..2*n-1} 1/k!.

a(n+1) = 2*n*(2*n+1)*a(n) + 2*n+2. (End)