There is a function FindSequenceFunction in Mathematica, that can identify a sequence of integers based on a few first elements. But what if I have a set of finite sequences sec[n] that grows with n? For example:

sec[0]={1}
sec[1]={1, 1}
sec[2]={1, 6, 1}
sec[3]={1, 15, 15, 1}
sec[4]={1, 28, 70, 28, 1}
sec[5]={1, 45, 210, 210, 45, 1}
sec[6]={1, 66, 495, 924, 495, 66, 1}
sec[7]={1, 91, 1001, 3003, 3003, 1001, 91, 1}
sec[8]={1, 120, 1820, 8008, 12870, 8008, 1820, 120, 1}

Is there a way to use Mathematica to find the general expression to continue this sequence of sequences? Thanks for any suggestion!

There is a function FindSequenceFunction in Mathematica, that can identify a sequence of integers based on a few first elements. But what if I have a set of finite sequences sec[n] that grows with n? For example:

sec[0]={1}
sec[1]={1, 1}
sec[2]={1, 6, 1}
sec[3]={1, 15, 15, 1}
sec[4]={1, 28, 70, 28, 1}
sec[5]={1, 45, 210, 210, 45, 1}
sec[6]={1, 66, 495, 924, 495, 66, 1}
sec[7]={1, 91, 1001, 3003, 3003, 1001, 91, 1}
sec[8]={1, 120, 1820, 8008, 12870, 8008, 1820, 120, 1}

Is there a way to use Mathematica to find the general expression to continue this sequence of sequences?