A374085 Number of sequences of length A062714(n) with symbols from {1, 2, 3, ..., n} which contains, as a subsequence, each possible ordering of the n symbols 1, 2, 3, ..., n.

1, 2, 42, 216

Offset: 1

Author

Chai Wah Wu, Jun 27 2024

Keywords

• nonn
• more
• hard

Comments

a(n) is a multiple of n!.

Examples

			a(1) = 1 as '1' is the only sequence of length A062714(1) = 1.
a(2) = 2 corresponding to the sequences of length A062714(2) = 3 : {'121', '212'}.
a(3) = 42 corresponding to the sequences of length A062714(3) = 7 : {'1213121', '1213212', '1231213', '1231231', '1231321', '1232123', '1232132', '1312131', '1312313', '1321231', '1321312', '1321321', '1323123', '1323132', '2123121', '2123212', '2131213', '2131231', '2132123', '2132132', '2132312', '2312132', '2312312', '2312321', '2313213', '2313231', '2321232', '2321323', '3121312', '3121321', '3123123', '3123132', '3123213', '3132131', '3132313', '3212312', '3212321', '3213123', '3213213', '3213231', '3231232', '3231323'}.
		

Crossrefs

Cf. A062714, A180632.