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 A298804 Triangle T(n,k) (1 <= k <= n) read by rows: A046936 with rows reversed and offset changed to 1. 4
 0, 1, 1, 3, 2, 1, 9, 6, 4, 3, 31, 22, 16, 12, 9, 121, 90, 68, 52, 40, 31, 523, 402, 312, 244, 192, 152, 121 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS This is another version of Moser's version (A046936) of Aitken's array (A011971). Although offset 0 is better for A011971 and A046936, for this version offset 1 is more appropriate. Comments from Don Knuth, Jan 29 2018 (Start): a(n,k) is the number of set partitions (i.e. equivalence classes) in which (i) 1 is not equivalent to 2, ..., nor k; and (ii) the last part, when parts are ordered by their smallest element, has size 1; (iii) that last part isn't simply "1". (Equivalently, n>1.) It's not difficult to prove this characterization of a(k,n). For example, if we know that there are 22 partitions of {1,2,3,4,5} with 1 inequivalent to 2, and 6 partitions of {1,2,3,4} with 1 inequivalent to 2, then there are 6 partitions of {1,2,3,4,5} with 1 inequivalent to 2 and 1 equivalent to 3. Hence there are 16 with 1 equivalent to neither 2 nor 3. The same property, but leaving out conditions (ii) and (iii), characterizes Pierce's triangular array A123346. (End) LINKS Table of n, a(n) for n=1..28. Don Knuth, Email to N. J. A. Sloane, Jan 29 2018 EXAMPLE Triangle begins: 0, 1, 1, 3, 2, 1, 9, 6, 4, 3, 31, 22, 16, 12, 9, 121, 90, 68, 52, 40, 31 523, 402, 312, 244, 192, 152, 121 ... CROSSREFS Cf. A011971, A040027, A046936, A123346. Sequence in context: A109267 A185416 A193918 * A155788 A108073 A057731 Adjacent sequences: A298801 A298802 A298803 * A298805 A298806 A298807 KEYWORD nonn,tabl,more AUTHOR N. J. A. Sloane, Jan 30 2018, following a suggestion from Don Knuth, Jan 29 2018. STATUS approved

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Last modified April 25 10:51 EDT 2024. Contains 371967 sequences. (Running on oeis4.)