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a(n) = n! * Sum_{k=1..n} H(k)*(n+1-k)!, where H(k) = Sum_{j=1..k} 1/j.
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%I #19 Nov 20 2018 05:22:50

%S 1,7,65,930,20814,693732,32312412,1996944912,157655618928,

%T 15457109916960,1841080739130720,261722785741833600,

%U 43758563047332750720,8498963447183108148480,1897379318289205012550400,482444035336741492040140800,138599348510645114991010560000

%N a(n) = n! * Sum_{k=1..n} H(k)*(n+1-k)!, where H(k) = Sum_{j=1..k} 1/j.

%H Vincenzo Librandi, <a href="/A109779/b109779.txt">Table of n, a(n) for n = 1..200</a>

%F E.g.f.: (hypergeom([1, 1], [], x)+x*hypergeom([2, 2], [], x))*log(1-x)/(x-1). - _Vladeta Jovovic_, Aug 17 2005

%t a[n_] := n! * Sum[(n+1-k)! * Sum[1/j, {j, 1, k}], {k, 1, n}]; Table[a[n], {n, 1, 30}] (* _Ryan Propper_, Sep 01 2005 *)

%o (PARI) a(n) = n!*sum(k=1, n, sum(j=1, k, 1/j)*(n+1-k)!); \\ _Michel Marcus_, Nov 20 2018

%Y Cf. A109780.

%K nonn

%O 1,2

%A _Leroy Quet_, Aug 13 2005

%E More terms from _Ryan Propper_, Sep 01 2005