%I #17 Jun 04 2019 10:37:43
%S 0,1,6,32,169,921,5248,31388,197133,1298804,8962070,64646382,
%T 486545028,3813611643,31075203744,262802902944,2303066401903,
%U 20883838079019,195682855232648,1892280736283390,18862445424597027,193603796552389848,2044036227150998116,22177186058234124636
%N a(n) is the total number of sum of weighted records over set partitions of [n].
%H Walaa Asakly, <a href="https://arxiv.org/abs/1906.00680">Sum of weighted records in set partitions</a>, arXiv:1906.00680 [math.CO], 2019.
%F a(n) = 3*(B(n+3) - B(n+2))/4 - (n+7/4)*B(n+1) - (n+1)*B(n)/2 where B(n) is the n-th Bell number, A000110(n).
%o (PARI) B(n) = sum(k=0, n, stirling(n, k, 2)); \\ A000110
%o a(n) = 3*(B(n+3) - B(n+2))/4 - (n+7/4)*B(n+1) - (n+1)*B(n)/2;
%Y Cf. A000110.
%K nonn
%O 0,3
%A _Michel Marcus_, Jun 04 2019
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