Solution to the Dancing School Problem with 8 girls and n+8 boys: f(8,n).

Terms

a(0) =1a(1) =9a(2) =221a(3) =2227a(4) =15458a(5) =80196a(6) =334072a(7) =1173240a(8) =3598120a(9) =9856552a(10) =24553080a(11) =56423032a(12) =121013800a(13) =244555560a(14) =469343992a(15) =860997880a(16) =1517994792a(17) =2583928360a(18) =4262971000a(19) =6839066232a(20) =10699415080a(21) =16362861352a(22) =24513820920a(23) =36042440440a(24) =52091711272a(25) =74112304680