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Partial sums of A058681.
0

%I #7 Jun 09 2023 21:23:26

%S 1,8,44,215,1028,5040,25931,141394,818940,5030489,32670830,223561960,

%T 1606504121,12086613500,94951417768,777028092855,6609770035768,

%U 58333927746852,533203742855027,5039919479205198,49191925330095240

%N Partial sums of A058681.

%C Partial sums of number of matroids of rank 2 on n labeled points. Partial sums of number of collections containing two or more nonempty subsets of {1,2,...n} that are pairwise disjoint. The subsequence of primes in this partial sum begins: 25931, 5030489.

%F a(n) = Sum_{i=2..n} A058681(i) = Sum_{i=2..n} (B(n+1) - 2^n), where B = Bell numbers (A000110).

%e a(11) = 1 + 7 + 36 + 171 + 813 + 4012 + 20891 + 115463 + 677546 + 4211549 = 5030489 is prime.

%t Accumulate[Table[BellB[n+1]-2^n,{n,2,30}]] (* _Harvey P. Dale_, Feb 14 2012 *)

%Y Cf. A000110, A058681.

%K easy,nonn

%O 2,2

%A _Jonathan Vos Post_, Apr 23 2010