Famous integer sequences

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Can you name the famous (nonnegative) integer sequences given their first terms?

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First termsSequence name
6, 28, 496, 8128, 33550336, 8589869056, …
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, …
0, 1, 36, 1225, 41616, 1413721, 48024900, …
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, …
70, 836, 4030, 5830, 7192, 7912, 9272, …
3, 7, 31, 127, 8191, 131071, 524287, …
1, 2, 6, 30, 210, 2310, 30030, 510510, …
1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, …
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, …
2, 7, 1, 8, 2, 8, 1, 8, 2, 8, 4, 5, 9, …
2, 5, 52, 88, 96, 120, 124, 146, 162, 188, …
1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9, 4, 8, …
First termsSequence name
0, 1, 11, 111, 1111, 11111, 111111, 1111111, …
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, …
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …
3, 5, 17, 257, 65537, 4294967297, …
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, …
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, …
0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, …
1, 2, 4, 6, 12, 24, 36, 48, 60, 120, …
1, 2, 6, 20, 70, 252, 924, 3432, 12870, …
0, 1, 8, 27, 64, 125, 216, 343, 512, 729, …
1, 1, 2, 6, 24, 120, 720, 5040, 40320, …

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