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Number of set partitions of [n] having exactly five pairs (m,m+1) such that m is in some block b and m+1 is in block b+1.
2

%I #5 Apr 14 2016 14:38:09

%S 0,1,21,242,2161,17081,127540,931343,6781012,49778592,370879817,

%T 2815885116,21840126520,173297901709,1407962621143,11717253906772,

%U 99896499620107,872434202618833,7803398795633086,71462039680103117,669812596793753200,6423126853283399476

%N Number of set partitions of [n] having exactly five pairs (m,m+1) such that m is in some block b and m+1 is in block b+1.

%H Alois P. Heinz, <a href="/A271792/b271792.txt">Table of n, a(n) for n = 5..300</a>

%e a(6) = 1: 1|2|3|4|5|6.

%e a(7) = 21: 12|3|4|5|6|7, 13|24|5|6|7, 1|23|4|5|6|7, 14|25|36|7, 1|24|35|6|7, 1|2|34|5|6|7, 15|26|37|4, 1|25|36|47, 1|2|35|46|7, 1|2|3|45|6|7, 16|27|3|4|5, 1|26|37|4|5, 1|2|36|47|5, 1|2|3|46|57, 1|2|3|4|56|7, 17|2|3|4|5|6, 1|27|3|4|5|6, 1|2|37|4|5|6, 1|2|3|47|5|6, 1|2|3|4|57|6, 1|2|3|4|5|67.

%Y Column k=5 of A185982.

%K nonn

%O 5,3

%A _Alois P. Heinz_, Apr 14 2016