%I #15 Dec 08 2019 08:13:03

%S 1,5,3,49,48,11,820,1030,404,50,21076,31050,16090,3510,274,773136,

%T 1277136,792540,233100,32724,1764,38402064,69261696,48943692,17498880,

%U 3361176,330624,13068,2483133696,4805827776,3752675136,1545593616,364984704,49672224,3622464,109584

%N Triangle of "Harmonic Coefficients" T(n,k), read by rows: (Sum_{i=1..n} T(n,i) * k^i) * k! / ((n+k)! * n!) = (Sum_{i=1..k} (1/i-1/(i+n)) = n * (Sum_{i=1..k} 1/(i*(i+n)))).

%F T(n, m) = n! * Sum_{k=1..m} ((-1)^(k+1) * S(n+1, m+1-k) * Sum_{i=1..n} i^(-k-1)), where S(n, m) are the unsigned Stirling numbers of the first kind.

%F T(n, m) = n! * (S(n+1, m+1) * Sum_{k=1..n} (1/k) - S(n+1, m+2)*(m+1)).

%e Triangle begins:

%e 1;

%e 5, 3;

%e 49, 48, 11;

%e 820, 1030, 404, 50;

%e ...

%K nonn,tabl,easy

%O 0,2

%A _Leroy Quet_.

%E Revised and more terms from _Sean A. Irvine_, Dec 07 2019