Number of possible positions for n discs on a standard 7 X 6 board of Connect-Four.

Terms

a(0) =1a(1) =7a(2) =56a(3) =252a(4) =1260a(5) =4620a(6) =18480a(7) =59815a(8) =206780a(9) =605934a(10) =1869840a(11) =5038572a(12) =14164920a(13) =35459424a(14) =91871208a(15) =214864650a(16) =516936420a(17) =1134183050a(18) =2546423880a(19) =5252058812a(20) =11031780760a(21) =21406686756a(22) =42121344720a(23) =76871042612a(24) =141627466344a(25) =242619996500a(26) =417750499600