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%I #12 Feb 06 2017 19:02:32
%S 1,1,5,39,16,1,369,120,12,2908,1000,98,19185,7474,1228,60,3,137200,
%T 63896,12448,1092,53,1022915,540562,120034,12676,590,4,7606043,
%U 4365686,1084022,140512,8836,250,5,55699672,34738058,9663366,1466724,124242,5984,166
%N Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape U; triangle T(n,k), n>=0, read by rows.
%C Sum_{k>0} k * T(n,k) = A247741(n).
%H Alois P. Heinz, <a href="/A247708/b247708.txt">Rows n = 0..175, flattened</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e T(3,2) = 1:
%e ._____.
%e | ._. |
%e |_| |_|
%e |_. ._|
%e | |_| |
%e |_____| .
%e Triangle T(n,k) begins:
%e 00 : 1;
%e 01 : 1;
%e 02 : 5;
%e 03 : 39, 16, 1;
%e 04 : 369, 120, 12;
%e 05 : 2908, 1000, 98;
%e 06 : 19185, 7474, 1228, 60, 3;
%e 07 : 137200, 63896, 12448, 1092, 53;
%e 08 : 1022915, 540562, 120034, 12676, 590, 4;
%e 09 : 7606043, 4365686, 1084022, 140512, 8836, 250, 5;
%e 10 : 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166;
%Y Row sums give A174249 or A233427(n,5).
%Y Column k=0 gives A247772.
%Y Cf. A247741.
%K nonn,tabf
%O 0,3
%A _Alois P. Heinz_, Sep 22 2014
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