Triangle of number of connected subgraphs of K(n,n) with m edges.

Terms

a(0) =1a(1) =4a(2) =1a(3) =81a(4) =78a(5) =36a(6) =9a(7) =1a(8) =4096a(9) =8424a(10) =9552a(11) =7464a(12) =4272a(13) =1812a(14) =560a(15) =120a(16) =16a(17) =1a(18) =390625a(19) =1359640a(20) =2696200a(21) =3880300a(22) =4394600a(23) =4059000a(24) =3111140a(25) =1994150a(26) =1070150a(27) =478800a(28) =176900a(29) =53120