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a(n) = A002105(n+1) - A005046(n), reduced tangent numbers minus the number of partitions of a 2*n-set into even blocks.
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%I #10 Aug 13 2019 07:05:52

%S 0,0,0,3,117,4500,199155,10499643,663488532,50115742365,4497657826905,

%T 476074241776188,58963860817626567,8475738174076417335,

%U 1402598717609785850700,265126817539686778513113,56822367893441673215117997,13712983199783483607459996660,3702793973661590950848375537915

%N a(n) = A002105(n+1) - A005046(n), reduced tangent numbers minus the number of partitions of a 2*n-set into even blocks.

%H Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BellTransform">The Bell transform</a>.

%F a(n) = (-2)^(n+1)*Euler(2*n+1, 0) - b(n) where b(n) is the sum of row 2*n + 1 of the Bell transform of n mod 2. The Bell transform is defined in A264428.

%p B := BellMatrix(n -> modp(n,2), 37): # defined in A264428.

%p b := n -> add(k, k in B[2*n+1]):

%p seq(euler(2*n+1, 0)*(-2)^(n+1) - b(n), n=0..18);

%Y Cf. A125107 (row 0 of A327000), A048742 (row 1 of A327000), this sequence (row 2 of A327000).

%Y Cf. A002105, A005046, A264428, A000182.

%K nonn

%O 0,4

%A _Peter Luschny_, Aug 13 2019