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A306900
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a(n) is the total number of sum of weighted records over set partitions of [n].
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0
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0, 1, 6, 32, 169, 921, 5248, 31388, 197133, 1298804, 8962070, 64646382, 486545028, 3813611643, 31075203744, 262802902944, 2303066401903, 20883838079019, 195682855232648, 1892280736283390, 18862445424597027, 193603796552389848, 2044036227150998116, 22177186058234124636
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OFFSET
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0,3
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LINKS
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FORMULA
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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).
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PROG
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(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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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