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A084417 Triangle read by rows: T(n,k)=sum((n+1-i)!*stirling2(n,n+1-i),i=1..k), n>=1, 1<=k<=n.

%I A084417 #7 Mar 30 2012 17:35:53
%S A084417 1,2,3,6,12,13,24,60,74,75,120,360,510,540,541,720,2520,4080,4620,
%T A084417 4682,4683,5040,20160,36960,45360,47166,47292,47293,40320,181440,
%U A084417 372960,498960,539784,545580,545834,545835,362880,1814400,4142880,6048000
%N A084417 Triangle read by rows: T(n,k)=sum((n+1-i)!*stirling2(n,n+1-i),i=1..k), n>=1, 1<=k<=n.
%C A084417 Interpolates between A000670 and factorials.
%F A084417 T(n, k)=sum((n+1-i)!*stirling2(n, n+1-i), i=1..k), n>=1, 1<=k<=n.
%e A084417 1;2,3;6,12,13;24,60,74,75;120,360,510,540,541;
%p A084417 with(combinat): T:=(n,k)->sum((n+1-i)!*stirling2(n,n+1-i),i=1..k): seq(seq(T(n,k),k=1..n),n=1..10);
%Y A084417 Mirror image of array in A084416.
%Y A084417 T(n, 1)=n!=A000142(n), T(n, n)=A000670(n), T(n, n-1)=A052875(n).
%K A084417 nonn,tabl,easy
%O A084417 1,2
%A A084417 _N. J. A. Sloane_, Jun 24 2003
%E A084417 Edited by _Emeric Deutsch_, May 11 2004