A307663 a(n) = (n-1)!*(Sum_{i=1..n} Sum_{j=1..i} binomial(i,j)*i/j).

1, 6, 41, 329, 3090, 33654, 420792, 5981688, 95782320, 1712555280, 33909364800, 737868052800, 17521164259200, 451126883894400, 12522623670144000, 372847351488998400, 11853064556660275200, 400718191717647820800, 14354714544806716416000, 543129329390299739136000, 21642934280974058207232000

Offset: 1

Author

Pedro Caceres, Apr 20 2019

Keywords

• nonn

Examples

			a(2) = 1! * (C(1,1)*1/1 + C(2,1)*2/1 + C(2,2)*2/2) = 6.
		

Links

• Sela Fried, A307663, 2024.

Programs

Mathematica

Array[(# - 1)!*Sum[Sum[Binomial[i, j] i/j, {j, i}], {i, #}] &, 21] (* Michael De Vlieger, Apr 21 2019 *)

PARI

a(n) = (n-1)!*sum(i=1, n, sum(j=1, i, binomial(i,j)*i/j)); \\ Michel Marcus, Apr 20 2019

Formula

Conjectures from Robert Israel, Oct 26 2020: (Start)

E.g.f. ((4*x^2 - 8*x + 5)*log(-x + 1))/(2*(x - 1)^2) - ((4*x^2 - 8*x + 5)*log(1 - 2*x))/(2*(x - 1)^2) + x*(-6 + 5*x)/(4*(x - 1)^2).

D-finite with recurrence 2*(n+3)*(n+2)*n*(n-2)*a(n) - (n+3)*(5*n^2-6*n-17)*a(n+1) + (4 n^2-n-29)* a(n+2) -(n-3)*a(n+3) = 0. (End)

The conjecture regarding the e.g.f. is true. See links. - Sela Fried, Jul 30 2024.