%I #23 Nov 14 2014 10:29:10

%S 1,3,22,600,78912,60963840,325173657600,13743074967552000,

%T 5190968541142056960000,19502847300506769948672000000,

%U 802654006697267902579055001600000000,395082050396018659026474786525020160000000000

%N 1!*2!*3!*...*n!*H(n); H(n) the n-th harmonic number.

%C Determinant of the n x n - Matrix A[i,j] with A[1,j]=1 (1<=j<=n) and A[i,j]=j^i (i>1, 1<=j<=n) [L. Theisinger].

%D L. Theisinger, Bemerkung über die harmonische Reihe. Monatshefte für Mathematik und Physik XXVI. Jahrgang (1915), 132-134.

%H Alois P. Heinz, <a href="/A195462/b195462.txt">Table of n, a(n) for n = 1..30</a>

%F a(n) = A000178(n)*A001008(n)/A002805(n).

%e a(4) = 1!*2!*3!*4!*H(4) = 1*2*6*24*(25/12) = 600.

%p a:= n-> mul(j^(n-j+1), j=2..n) * add(1/k, k=1..n):

%p seq(a(n), n=1..15); # _Alois P. Heinz_, Sep 21 2011

%Y Cf. A000178, A001008, A002805.

%K nonn,easy

%O 1,2

%A _Franz Vrabec_, Sep 21 2011