A326995 a(n) = A002105(n+1) - A005046(n), reduced tangent numbers minus the number of partitions of a 2*n-set into even blocks.

0, 0, 0, 3, 117, 4500, 199155, 10499643, 663488532, 50115742365, 4497657826905, 476074241776188, 58963860817626567, 8475738174076417335, 1402598717609785850700, 265126817539686778513113, 56822367893441673215117997, 13712983199783483607459996660, 3702793973661590950848375537915

Offset: 0

Author

Peter Luschny, Aug 13 2019

Keywords

• nonn

Links

• Peter Luschny, The Bell transform.

Crossrefs

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

Cf. A002105, A005046, A264428, A000182.

Programs

Maple

B := BellMatrix(n -> modp(n,2), 37): # defined in A264428.
b := n -> add(k, k in B[2*n+1]):
seq(euler(2*n+1, 0)*(-2)^(n+1) - b(n), n=0..18);

Formula

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.