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%I #31 Oct 04 2020 02:44:56
%S 1,2,8,57,806,20840,1038266,97115638,17213517207,5768580741287
%N a(n) is the number of ways to tile a size n staircase polyomino with staircase polyominoes.
%C A size-n staircase polynomo is a polyomino consisting of n left-aligned rows in increasing length of 1, 2, ..., n. Rotations of staircase polyominoes are also polyominoes.
%H Code Golf Stack Exchange user "Bubbler", <a href="https://codegolf.stackexchange.com/q/210748/53884">Tiling a staircase with staircases</a>.
%e For n = 3 the a(3) = 8 tilings are:
%e +---+ +---+ +---+ +---+
%e | | | | | | | |
%e +---+---+ + +---+ +---+---+ +---+---+
%e | | | | | | | | | | |
%e +---+---+---+, +---+---+---+, + +---+---+, +---+ +---+,
%e | | | | | | | | | | | | | |
%e +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
%e +---+ +---+ +---+ +---+
%e | | | | | | | |
%e +---+---+ +---+---+ +---+---+ + +---+
%e | | | | | | | | |
%e +---+ +---+, + +---+---+, +---+ +---+, + +---+.
%e | | | | | | | | | | | | |
%e +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
%Y Cf. A000105, A045846, A219924, A254414, A335547.
%K nonn,more
%O 1,2
%A _Peter Kagey_, Sep 08 2020
%E a(8) from _Seiichi Manyama_, Sep 09 2020
%E a(9)-a(10) from _Bert Dobbelaere_, Sep 12 2020