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A306900 a(n) is the total number of sum of weighted records over set partitions of [n]. 0

%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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Last modified March 29 02:13 EDT 2024. Contains 371264 sequences. (Running on oeis4.)