A109780 - OEIS

%I #20 Nov 20 2018 05:23:14

%S 1,5,32,310,4924,126648,4869192,258608880,17973530784,1576566817920,

%T 170028329630400,22092970356011520,3402396234446595840,

%U 612619882946124157440,127484451712085785228800,30358069092698014483200000,8201548600725828770272972800

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

%H Vincenzo Librandi, <a href="/A109780/b109780.txt">Table of n, a(n) for n = 1..200</a>

%F E.g.f.: hypergeom([1, 1], [], x)*log(1-x)/(x-1). - _Vladeta Jovovic_, Aug 16 2005

%t f[n_] := n! * Sum[(n-k)! * Sum[1/j, {j, 1, k}], {k, 1, n}]; Table[f[n], {n, 1, 30}] (* _Ryan Propper_, Aug 18 2005 *)

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

%Y Cf. A109779.

%K nonn

%O 1,2

%A _Leroy Quet_, Aug 13 2005

%E More terms from _Ryan Propper_, Aug 18 2005