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

0, 1, 6, 32, 169, 921, 5248, 31388, 197133, 1298804, 8962070, 64646382, 486545028, 3813611643, 31075203744, 262802902944, 2303066401903, 20883838079019, 195682855232648, 1892280736283390, 18862445424597027, 193603796552389848, 2044036227150998116, 22177186058234124636

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Walaa Asakly, Sum of weighted records in set partitions, arXiv:1906.00680 [math.CO], 2019.

Formula

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).

Prog

(PARI) B(n) = sum(k=0, n, stirling(n, k, 2)); \\ A000110
a(n) = 3*(B(n+3) - B(n+2))/4 - (n+7/4)*B(n+1) - (n+1)*B(n)/2;

Crossrefs

Cf. A000110.

Sequence in context: A082585 A084326 A199699 * A137637 A125190 A264460

Adjacent sequences: A306897 A306898 A306899 * A306901 A306902 A306903

Keyword

nonn

Author

Michel Marcus, Jun 04 2019

Status

approved