%I A145460
%S A145460 1,1,1,1,1,2,1,0,3,5,1,0,1,10,15,1,0,0,3,41,52,1,0,0,1,9,196,203,1,0,0,
%T A145460 0,4,40,1057,877,1,0,0,0,1,10,210,6322,4140,1,0,0,0,0,5,30,1176,41393,
%U A145460 21147,1,0,0,0,0,1,15,175,7273,293608,115975,1,0,0,0,0,0,6,35,1176
%N A145460 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where sequence 
               a_k of column k is the exponential transform of C(n,k).
%C A145460 A(n,k) is also the number of ways of placing n labeled balls into indistinguishable 
               boxes, where in each filled box k balls are seen at the top. E.g. 
               A(3,1)=10:
%C A145460 |1.| |2.| |3.| |1|2| |1|2| |1|3| |1|3| |2|3| |2|3| |1|2|3|
%C A145460 |23| |13| |12| |3|.| |.|3| |2|.| |.|2| |1|.| |.|1| |.|.|.|
%C A145460 +--+ +--+ +--+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+-+
%H A145460 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%e A145460 Square array A(n,k) begins:
%e A145460 1 1 1 1 1 1 ...
%e A145460 1 1 0 0 0 0 ...
%e A145460 2 3 1 0 0 0 ...
%e A145460 5 10 3 1 0 0 ...
%e A145460 15 41 9 4 1 0 ...
%e A145460 52 196 40 10 5 1 ...
%p A145460 exptr:= proc(p) local g; g:= proc(n) option remember; local j; `if` (n=0, 
               1, add (binomial (n-1, j-1) *p(j) *g(n-j), j=1..n)) end: end: A:= 
               (n,k)-> exptr (i-> binomial (i, k)) (n): seq (seq (A(n, d-n), n=0..d), 
               d=0..12);
%Y A145460 Columns 0-9 give: A000110, A000248, A133189 A145453, A145454, A145455, 
               A145456, A145457, A145458, A145459. Cf.: A007318, A143398.
%Y A145460 Sequence in context: A135488 A099493 A088523 this_sequence A035543 A105546 
               A059297
%Y A145460 Adjacent sequences: A145457 A145458 A145459 this_sequence A145461 A145462 
               A145463
%K A145460 nonn,tabl
%O A145460 0,6
%A A145460 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 10 2008